Courses and Events for Math Students and Early Career Researchers

Institute for Mathematical Sciences/National University of Singapore

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Institute for Mathematical Sciences/National University of Singapore

Engineering (general),    Applied Mathematics (in general)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Graph Theory and Combinatorics,    Geometry and Topology

University of Luxembourg

The ERA Chair Team organises a Winter School on Mathematical Statistics from 7 to 11 December 2020 at the University of Luxembourg on Belval campus. This school is aimed at young researchers (PhD students and early postdocs) and practitioners alike and offers an excellent opportunity to learn about recent and important developments in mathematical statistics directly from leaders in their respective fields.

Institute for Mathematical Sciences/National University of Singapore

This workshop is devoted to the theory of representations of reductive groups over local fields.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Vermont Complex Systems Center at the University of Vermont

The Complex Networks Winter Workshop (CNWW) is a week-long international school that offers an extraordinary opportunity for participants to engage in rigorous transdisciplinary complexity science research alongside some of the top researchers in the field of networks. The CNWW is designed for graduate students, postdoctoral fellows, and professionals. The lectures will present open problems and recent advances in the field of complex networks. Participants of this program will collaborate in small transdisciplinary research groups involving other participants as well as faculty. All course lectures will be given in English.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Algebra,    Geometry and Topology

Institute for Mathematical Sciences/National University of Singapore

In this two-week program, we explore the interactions between geometric group theory, geometric structures and Anosov representations. Geometric group theory, in the broadest sense, seeks to understand the structure of groups through their actions on objects with geometric meaning. Conversely, one can take a known group and attempt to understand all its geometrically meaningful actions. One natural notion that arises in this setting is an Anosov representation, which came about as an attempt to describe what it means for the action of a discrete group on a homogeneous space to be geometrically well behaved. Also, in his Erlangen program, Felix Klein viewed geometry as a space which is invariant under a group of transformations. This gave rise to the notion of a geometric structure, which gives yet another notion of a geometrically meaningful action of a group on a homogeneous space.

Group Theory,    Geometry and Topology

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Banff's new workshop on Continuum models and optimisation for deep neural networks brings together scientists to discuss the foundations of our digital revolution, and to investigate the reliability of their results. As often, mathematics is the fundamental tool to examine today's challenges. Mathematics structures knowledge and identifies the strengths and limitations of deep learning algorithms. A better understanding of the maths behind deep learning helps us to develop more efficient algorithms and to put safety critical industrial areas such as autonomous driving on a firm ground.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Calculus, Differential Equations and Integration,    Numerical Analysis and Computational Mathematics

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

It is the goal of this workshop to bring together the leading experts in various fields of a posteriori error control to create synergies for combining the separated know-how towards the ultimate goal of efficient and reliable modelling of complex physical phenomena and real-world applications.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Institute for Mathematical Sciences/National University of Singapore

This is a two-week program gathering mathematicians and physicists interested in the statistical physics of strongly correlated and long range random particle systems. These particle systems include Gibbs point processes such as Coulomb gases, determinantal point process, eigenvalues of random matrices, etc. They are linked to mathematical long-standing challenges such as the crystallization and best packing conjectures among others. One aspect that we want to put forward in this meeting is that the pioneering tools from classical statistical mechanics à la Ruelle, Lanford, Lebowitz may not have been used enough for the study of these particle systems yet.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

This workshop will address emerging challenges in human-environment interactions. Ecosystem services are under threat due to human activities. We will model feedbacks between the environment and human behaviour with a view to illuminating the mathematical structures that govern interactions. Our goal is to develop methods that can suggest a path forward in improving the interactions between humans and the environment.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The physical sciences have entered the era of big data, and particle physics is no exception. Extremely powerful particle colliders, telescopes observing light across the energy spectrum, and precise underground experiments have been running for years and have produced remarkably detailed and complex data sets. While no definitive signal of new physics has yet emerged from these experiments, it is quite possible that hints of new phenomena are hidden in these results, only missed due to the limitations of our analysis methods. In this workshop, we will bring together statisticians and physicists to discuss novel methods of data analysis, with a focus on machine learning, in which computers are programmed to think in ways akin to humans. We will launch the development of new computer tools that will allow us to overcome current computational limitations and fully test particle physics theories against all available data, potentially leading to discoveries that will shed light on some of the most profound questions in physics.

Applied Mathematics (in general),    Computational Physics and Numerical Simulation

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The subject of magnetic monopoles is by now classic in both physics and mathematics. Since intense advancements in mid 1970’s, numerous deep connections to theoretical physics, algebraic geometry, and geometric analysis have been discovered. Nonetheless, many important problems remain unsolved. Recently, monopoles acquired new significance in areas such as string theory, the Seiberg--Witten theory, quantum gauge-theory spaces of vacua, knot invariants, and the Geometric Langlands correspondence. This workshop brings together experts from around the world advancing very different perspectives, identify important open problems, and connecting diverse methods used by different groups.

Mathematical Physics,    High Energy Physics, Particles and Fields

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Uncertainty pervades all areas of the natural sciences, engineering, and operations research. Such uncertainty may arise due to noisy measurements, model ambiguity, or unknown parameters. Moreover, optimal decision making under uncertainty is crucial to arrive at reliable solutions, which are resilient to catastrophe. Despite the inherent need to do so, including uncertainty in our models in the form of random parameters leads to a veritable explosion in the dimension of the resulting optimization or control problems; especially for models of complex engineering systems. Recent advances in the fields of uncertainty quantification and machine learning present exciting opportunities to help combat this curse of dimensionality. This workshop is intended is to join researchers in optimization under uncertainty, uncertainty quantification, and machine learning, whose work stands to benefit from cutting-edge machine learning techniques for intricate, data-driven models of real-world phenomena.

Operational research,    Software Agents and Intelligent Agents in Artificial Intelligence

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Applied Mathematics (in general),    Mathematical Physics

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

What could be a bigger source of "big data" than the entire Universe? Researchers in statistics and computer science are developing new methods to analyse the "big data" that companies and governments want to understand. To test out these methods they need big datasets that everyone can share - and new astronomical telescopes just happen to be gearing up to generate observations of billions of stars and galaxies that fit the bill. Insights from statistics will help astrophysicists to get the most out of these observations. The Astrostatistics 2021 workshop will bring together statisticians and astrophysicists to learn the technical languages of the two fields and identify how to work together to combine the excitement of space with big data.

Probability and Statistics, Game Theory,    Astronomy, Astrophysics and Cosmology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Neural Networks and Artificial Intelligence, Machine Learning,    Analysis

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The workshop will bring together some of the world's top experts and promising young researchers working at the interface of Stochastics and Geometry, broadly understood. Through expository talks and research presentations, the workshop will give a vibrant overview of the most recent developments in the interaction between analysis, geometry and stochastic analysis. The focus of the workshop will be different approaches to random processes in geometric settings, with emphasis on problems on heat kernel analysis on finite- and infinite-dimensional manifolds, sometimes equipped with degenerate geometries, as well as random matrices and non-commutative probability and geometric rough paths. Another objective of the workshop is to identify fundamental open problems in this area that are motivated by mathematical physics and other potential applications. We plan to maintain geographic diversity and also to invite some of the most promising junior mathematicians.

Probability and Statistics, Game Theory,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Rich mathematical structures appear in supersymmetric quantum field theories. These provide new perspectives on deep mathematics while at the same time allow for a better understanding of the quantum field theories. This workshop brings together experts from different areas in mathematics and theoretical physics with the aim of deepening our understanding and to foster new interdisciplinary collaborations.

High Energy Physics, Particles and Fields,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Technological advances have revolutionized our ability to observe the evolution of infections that are posing major global health challenges. However, using these new and high-resolution sources of data to improve health requires new theory -- new mathematical structures to understand patterns of ancestry and evolution in infectious diseases, new ways to map how antibiotic resistance emerges and spreads and new methods to combine data, modelling, inference and machine learning. This workshop will bring together mathematicians and statisticians, methods developers and biologists gathering state-of-the-art large datasets in pathogen genomics. The aims are to share not only mathematics and methods, but upcoming challenges and aims, and to ensure that large genomic datasets and the people that gather them have a voice in shaping methods and models towards the questions of the highest importance for pathogen evolution and ultimately for health.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The researchers participating in this workshop come from several mathematical subdisciplines, including combinatorics, algebraic geometry, and theoretical computer science. Their work and common interest here is to investigate new interactions between discrete mathematics, algebra, algebraic geometry, tropical geometry, and combinatorial algorithms. Some participants have collaborated before in smaller groups, but this meeting will provide an opportunity to work together more intensively. Several recent mathematical breakthroughs will be highlighted in the workshop, including the recent resolution of some long-standing open problems about graphs and matroids. These breakthroughs used a surprising combination of interdisciplinary techniques which the organizers expect to have exciting further applications.

Graph Theory and Combinatorics,    Information Theory, Foundations of Computer Science

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Recently, the study of Hénon maps has undergone new exciting developments, like the recent proof of the existence of wandering domain for complex Hénon maps. This result was achieved by mixing techniques from different parts of dynamics, namely real and complex. In this workshop we intend to pursue this trend by bringing together experts on real, complex and non-archimedean dynamics to get new perspectives in the study of Hénon maps.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Recently a variety of state-of-the-art methods in machine learning and artificial intelligence have been developed motivated by techniques from Stein’s method, a successful tool from the field of probability theory. These methods have enabled efficient analysis of the large amounts of data being produced in several scientific fields, like neuroscience, information technology, and finance. Motivated by this success, there has been an ever increasing interest in exploring further connections between Stein’s method and machine learning. The focus of this workshop is to consolidate isolated efforts and develop a theoretically principled inferential and computational framework via Stein's method for analyzing increasingly complex models and data objects. This workshop is intended to bring together prominent and promising young and diverse researchers working on Stein’s method and machine learning, and to charter the path for future development in the field.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

In recent years, big data has become a major challenge for the state of the art computational methods and algorithms that are used for extracting meaningful information. This dilemma stimulates the exchange of ideas necessary to generate new directions in big data inverse problems.This workshop intends to provide a platform for researchers from diverse backgrounds to discuss novel techniques for big data inverse problems with benefits to various fields of data science.

Modeling and Simulation,    Information & Knowledge Management, Big Data Computing

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

CIRM – Centre International de Rencontres Mathématiques

CIRM IHP PROGRAM

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

One of the most fundamental notions when studying functions of a real variable is the rate of change of a function, as measured by its derivative. Geometrically, the derivative is the slope of the tangent line. Both the notion of the derivative and the tangent line (or more generally, the tangent bundle of a smooth manifold) can be defined purely axiomatically because of the underlying structure of the category of smooth functions. The derivative, for example, is determined by its properties (such as the sum and product formulae for differentiation, the chain rule, etc.). This structural approach to the derivative leads to the notion of a differential category. When working with models of differential categories such as smooth functions, the listed properties seem like natural consequence of the model. On the contrary, the differential category structure shows that these properties determine the structure of the derivative, rather than the other way around.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematical Logic and Foundations,    Information Theory, Foundations of Computer Science

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The mathematical description of the behaviour of typical fluids, like water at room temperature, was one of the great scientific breakthroughs of the 19th century. Understanding and applying the equations that describe these fluid drove many developments in mathematics for the next 100 years. Later, with the advent of modern computing, new fields of mathematics emerged devoted to designing algorithms to simulate these flows. This simulation capability has revolutionised many fields of engineering: no car, aeroplane, bridge, or stent is built without it.

Modeling and Simulation,    Mechanics, Rheology and Tribology

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

An essential paradigm in science is solving a problem through the study of its symmetries. Whether dealing with a chemical, physical, or mathematical system, its symmetries are intimately related to the conservation laws characterizing the system itself. Therefore, their study leads us to its full understanding. Quantum groups are deformations of the most elementary symmetries in Nature, describing, for example, infinitesimal layers of ice. They first appeared in the eighties as symmetries of one and two-dimensional statistical mechanical models and are nowadays ubiquitous objects in mathematics. Quantum groups represent only an instance of the more general Theory of Quantization, in which the procedure of "deforming" classical structures gives rise to their "quantum" analog. This theory proved soon to have spectacular connections with many and only apparently unrelated areas of mathematics and physics, especially in representation theory (as described above), algebraic geometry (in particular the theory of moduli spaces), and theoretical physics (e.g. gauge theory). The present workshop aims to provide a survey of the state of the art of the Quantization Theory, with a special emphasis on using advanced techniques from (derived) algebraic geometry to the realm of Quantization.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

This workshop will reunite specialists of stochastic control and economic theory, who will work and explore how recent theoretical developments in their respective fields can be applied to these newly identified problems.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Privacy concerns are becoming a major obstacle to using data, and it is often unclear how current regulations should translate into technology. Over the last decade, differential privacy has emerged as the de facto algorithmic gold-standard in privacy-preserving data analysis, enabling analysis of sensitive data with rigorous privacy guarantees. It is a parameterized privacy notion, and tuning this privacy parameter allows an analyst to smoothly tradeoff between privacy to the individual with accuracy of the analysis. Much of the theoretical work on differential privacy has purposely left this parameter as a free variable that should be chosen based upon the context of data use. Contextual integrity is a framework for formalizing context of data use, and offers a descriptive categorization of information flows as either appropriate or inappropriate based upon the context and cultural norms. This workshop will combine tools from differential privacy and contextual integrity to develop context-based prescriptions for the use and implementation of differential privacy. It will bring together a multi-disciplinary team of privacy researchers from computer science, information science, statistics, business, law, and public policy to address this multifaceted challenge.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The aim of this workshop is to bring together experts on many developing perspectives on knot homology (physical, geometric and algebraic) to draw connections between them, and to explore applications.

Geometry and Topology,    Algebra

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Conformal geometry is the study of properties of spaces and mappings which depend on the measurement of angles but not of lengths. An example is the stereographic projection mapping from a sphere to a plane, which distorts lengths but preserves angles. Mathematicians have made much progress in recent years in the study of conformal geometry by using and developing new tools and methods from a variety of mathematical fields, including analysis, non-linear PDE and topology. This workshop will bring together experts from a variety of mathematical backgrounds with the goal of furthering our understanding of conformal geometry and its complex number analogue, CR geometry.

Geometry and Topology,    Calculus, Differential Equations and Integration

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The presence of singularity in mathematics and physics is an omnipresent phenomena which is the subject of an enormous amount of current research. One reason for this is that techniques which are useful and well understood in the context of smooth spaces do not carry over automatically to singular spaces in general. Depending on the type of singularity involved, one might find that a theorem which is true in the smooth setting requires modification even to make sense in a particular singular setting, and a singular object with extra structure may lead to a generalization of a theorem in which that extra structure plays a role.

Mathematical Physics,    Analysis

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Institute for Mathematical Sciences/National University of Singapore

This is a one-week program gathering mathematicians, engineers, and scientists interested in reduced order models and methods (ROMs) for systems of partial differential equations. The general idea behind ROMs is to derive a low-dimensional model from a high-dimensional model, by integrating techniques from data science, modeling, and simulation, in order to obtain accurate and reliable results at greatly reduced computational costs.

Applied Mathematics (in general),    Analysis

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Cells are the fundamental building blocks of life. Recent advancement in biotechnology has allow us to peek inside this every cell to better understand of biology and human disease. Single cell technology also generates big and complex data and brings about new data science challenges of computational and life scientists. The objective of this workshop is to bring together international leaders in diverse disciplines including mathematical, statistical, computational, biological and medical in an collaborative atmosphere to develop collaborative capacity that will tackle various underlying data science challenges in single cell research.

Molecular Biology,    Biophysics, Medical Physics

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

In this 5-day workshop, we shall bring the fields leaders, both theoretical and observational, together across the boundaries of several different fields, to discuss the important issues about black hole physics and gravitational wave astronomy in particular, and quantum field theory and quantum gravity in general. The workshop is very timely and important, and has been already received strong support from various leaders of the fields.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop focuses on the interaction between algebraic K-theory and chromatic homotopy theory. Algebraic K theory translates fundamental arithmetic and geometric information about a ring or scheme into homotopy theory. The chromatic perspective is a fundamental organizing principle of homotopy theory, decomposing a space or spectrum into certain `prime localizations'. Recent major advances use these localizations to prove descent results for algebraic K theory, or give vanishing results for K-theory in certain cases. This conference gathers mathematicians working in algebraic K-theory and in chromatic homotopy theory to explore these recent advances, work on open problems, and set the syllabus for future work in the field.

Institute for Mathematical Sciences/National University of Singapore

MRSI – Mathematical Sciences Research Institute, Berkeley | Centre de Recherches Mathematiques, Montreal

The courses in this summer school focus on mathematical models of group dynamics, how to describe their dynamics and their scaling limits, and the connection to discrete and continuous optimization problems.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

New experiments are challenging our conventional understanding of past, present, and future in the quantum world. This workshop will, therefore, explore the very foundations of our understanding of space, time, and gravity by looking at new mathematical concepts and methods related to the quantum processes of measuring location, orientation, speed, cause and effect. We expect to forge a path that blends together new ideas on how our description of the structure of space and time must be modified to fully understand how to combine gravity with quantum physics.

High Energy Physics, Particles and Fields,    Quantum Mechanics and Quantum Information Theory

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

A common intuition in dynamical systems is that systems with low complexity should have some sort of structure, while systems with high complexity should exhibit more randomness. We explore this notion in various settings, particularly focussing on recent developments in ergodic theory and symbolic dynamics that are related to combinatorial, number theoretic, and algebraic problems. Fine properties of sequences of numbers can be studied via dynamics, relating the complexity of the sequence to hidden structures it contains. The proposed meeting will cover such recent evelopments, bringing together mathematicians from a variety of fields, including ergodic theory, symbolic dynamics, number theory, and group theory to discuss on long-standing open problems that have implications for these fields.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Mathematical billiards are a fast growing field of the modern theory of dynamical systems and a deep source of insights, methods and examples in dynamics. It has greatly impacted many areas, ranging from integrable Hamiltonian systems and KAM theory, hyperbolic (chaotic) systems, to Teichm\"uller dynamics. It has also stimulated much recent applied research in such areas of mathematical physics as equilibrium and non-equilibrium statistical mechanics and quantum theory. The proposed workshop will bring together leading mathematicians, mathematical physicists, and younger researchers whose work is connected to the theory and applications of billiard dynamics from a variety of perspectives. Topics will include new modalities of billiard systems, with special attention given to applications to statistical physics such as, for example, the study of classical and quantum transport phenomena.

Complex Systems, Chaos and Self-Organisation,    Thermodynamics, Fluid Dynamics and Statistical Physics

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Fluid-driven crack propagation is the process by which pressurized fluid drives cracks through solid materials. Such a process is not only central to hydraulic fracture stimulation of oil and gas wells, but also it describes movement of molten rock through the Earth’s crust and water through the subsurface of glacial ice sheets. Hence, there is significant, and hitherto relatively untapped, potential for multidisciplinary investigation. Furthermore, the underlying mathematical problem is challenging even for simple propagation geometries and ignoring variability in material properties of the rock and/or ice sheet. When realistic variability and complexity is considered, the problem exceeds the capabilities of current computer simulation tools. To address these concerns, the objective of this workshop is to convene a BIRS Workshop of Applied Mathematicians, Geo-Scientists, and Engineers from Academia and Industry to accelerate the development of the state-of-the-art tools to analyze the evolution of fluid-driven cracks that propagate in complex solid media.

Applied Mathematics (in general),    Geophysics and Geology

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Fluids that exhibit physical behaviours which are not Newtonian are extremely common in nature and in industrial contexts. These occur in many processes underlying natural resource industries (mining, oil and gas). These are key in manufacturing industries such as polymer processing and in new environmentally-driven manufacturing products such as printing/layering in battery manufacture, coating flows, drug and droplet encapsulation and many bio-fluid applications (e.g. blood, mucus, semen, synovial fluids). This workshop brings together mathematically oriented scientists and engineers to work on these societally important issues.

Thermodynamics, Fluid Dynamics and Statistical Physics,    Computational Physics and Numerical Simulation

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

MRSI – Mathematical Sciences Research Institute, Berkeley

This summer school will introduce the participants to two of the main techniques in the subject: (i) the filtration method to prove algebraic degeneracy of integral points by means of the subspace theorem, leading to special cases of conjectures by Bombieri, Lang, and Vojta, and (ii) unlikely intersections through o-minimality and bi-algebraic geometry, leading to results in the context of the Manin-Mumford conjecture, the André-Oort conjecture, and generalizations. This SGS should provide an entry point to a very active research area in modern number theory.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

We will aim to create new mathematical models of complex fluids that can bridge length and time scales, and study novel ways to model entanglement of polymers and filaments. We stress that the novelty of this workshop consists not only in bringing together an interdisciplinary array of scientists, but bridging the gap between what has been traditionally catalogued as pure and applied mathematics.

Applied Mathematics (in general),    Condensed Matter Physics and Materials

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The mathematics of optimal transport (OT) has grown to become a unifying theme in many scientific disciplines, from solving purely mathematical problems of analysis, geometry, and partial differential equations to developing revolutionary new methods in economics, statistics, machine learning and artificial intelligence. In the last decade, the impact of optimal transport in the study of geometry was highlighted by two Fields medals (Villani 2010, Figalli 2018). On the other hand, OT has established itself as a viable alternative to classical maximum likelihood based methods in statistics and data science. Other notable applications include generative adversarial network (GAN) in machine learning (Wasserstein GAN), new applications to stem cell biology, and economic applications such as generalizations of the Nobel prize winning Gale-Shapley algorithm, online auctions, and option pricing.

Applied Mathematics (in general),    General Mathematical Research and Multidisciplinary Events

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

A mathematical knot can be thought of as a piece of knotted string with ends attached. This knotted circle is allowed to move freely in space as long as it does not pass through itself. In recent years the study of knots has gained momentum through a series of applications, for instance in physics and in molecular biology. Such applications bring new urgency to certain classical questions pertaining to knots and how they sit inside 3-dimensional space. Much like a knotted wand dipped into liquid soap will bound a bubble, mathematical knots sitting in 3-dimensional space bound surfaces. Studying pairs of the form (knot, surface) sitting in 3-dimensional space rather than just knots, provides additional structure to better grasp basic questions, such as whether or not a given knot can be untangled and if so how.

Geometry and Topology,    Algebra

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Geometry and Topology,    Algebra

MRSI – Mathematical Sciences Research Institute, Berkeley

This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.

Applied Mathematics (in general),    Information & Knowledge Management, Big Data Computing

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop will study this question for systems of geometric origin. One example of this is a particle bouncing inside a region -- think of a ball bouncing around a billiard table, or a light beam bouncing around a room whose walls are mirrors. If the walls are flat then the behavior is fairly predictable, but if they are curved then one often observes random-looking behavior in the long run. Or imagine walking in a straight line along a surface; if the surface is flat then changing the starting point a little will lead to a predictable change in the trajectory. However, if the surface is curved like a saddle then different trajectories will spread out and your location after walking for a long time will eventually seem to be random. The task of giving precise descriptions of systems such as these requires a more complete development of the theory of thermodynamic formalism for systems of geometric origin, which is precisely the goal of this workshop.

Mathematical Physics,    Thermodynamics, Fluid Dynamics and Statistical Physics

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Analysis,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Calculus, Differential Equations and Integration,    Numerical Analysis and Computational Mathematics

Institute of Mathematics of the University of Seville

This EURO PhD School (EPS) will focus on giving participants advanced training on Data Driven Decision Making. There will be a methodological as well as an applied component to this EPS. Methodological training on the role of Mathematical Optimization in Data Science will be given in the format of lectures and computer workshops. The lectures will highlight the mathematical and statistical modeling and numerical optimization behind data analysis and data visualization tools. The computer workshops will make this knowledge actionable. Applications of the acquired knowledge to the modeling of specific industrial problems will be presented by professionals from industry and worked out by the PhD students. Mathematical and statistical models and numerical solution approaches will be developed and communicated, following a collaborative approach, in which the PhD students will work in small groups under the guidance of the instructors.

MRSI – Mathematical Sciences Research Institute, Berkeley | ETH Zurich, Switzerland

This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

In arithmetic geometry, one studies solutions to polynomial equations defined with arithmetically interesting coefficients, such as integers or rational numbers. One way to study such objects, which has seen tremendous success in the last several decades, is by investigating their symmetries. Quite surprisingly, in several interesting situations, many of the geometric and arithmetic properties of the objects in question are actually controlled by the object’s symmetries.

Geometry and Topology,    Group Theory

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

MRSI – Mathematical Sciences Research Institute, Berkeley | University of Oxford, United Kingdom

The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.

Geometry and Topology,    Analysis

MRSI – Mathematical Sciences Research Institute, Berkeley

The goal of the summer school is to introduce students to the foundational aspects of gauge theory, and explore their relations to geometric analysis and low-dimensional topology. By the end of the two-week program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the Yang-Mills ASD equations, the Seiberg-Witten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.

Algebra,    Geometry and Topology

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

There is an age-old relationship between arithmetic and geometry, going back at least to Euclid's Elements. Historically, it has usually been geometry that has been used to enrich our understanding of arithmetic, but the purpose of this workshop is to study the flow of information in the other direction. Namely, how can arithmetic enhance our understanding of geometry? This meeting will bring together researchers from both sides of the partnership, to explore ways to bind the two fields ever closer together.

Geometry and Topology,    Number Theory, Arithmetic

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Analysis,    Systems theory, Control and Automation

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

One focus of modern number theory is to study symmetries of numbers that are roots of polynomial equations. Collections of such symmetries are called Galois groups, and they often encode interesting arithmetical information. The theory of Galois representations provides a way to understand these Galois groups and in particular, how they interact with other areas of mathematics. This workshop will investigate how these Galois representations can be put together into families, and search for new arithmetic applications of these families.

Number Theory, Arithmetic,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

MRSI – Mathematical Sciences Research Institute, Berkeley | National Center for Theoretical Sciences, Taipei, Taiwan

The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

MRSI – Mathematical Sciences Research Institute, Berkeley

This Summer Graduate School will cover basic tools that are instrumental in Random Conformal Geometry (the investigation of analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics) and are at the foundation of the subsequent semester-long program "The Analysis and Geometry of Random Spaces". Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.

Algebra,    Geometry and Topology

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The workshop brings together top experts in the field, and creates an environment where all the latest ideas, intuition and techniques can be shared and refined. Another important goal of the proposed workshop is to introduce junior researchers to a highly active area of research in PDEs of fluid dynamics. We will give preferences to young researchers when inviting speakers to the workshop.

Mathematical Physics,    Thermodynamics, Fluid Dynamics and Statistical Physics

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Algebraic dynamics is the study of discrete dynamical systems on algebraic varieties. It has its origins in complex dynamics, where one studies self-maps of complex varieties, and now encompasses dynamical systems defined over global fields. In recent years, researchers have fruitfully investigated the latter by applying number-theoretic techniques, particularly those of Diophantine approximation and geometry, subfields which study the metric and geometric behavior of rational or algebraic points of a variety.

Algebra,    Modeling and Simulation

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The purpose of this workshop is to bring together specialists in operator theory and complex analysis in several variables, with the aim of surveying recent developments and fostering new interactions between researchers in these subjects. Specific topics featured in this workshop include non-commutative function theory and its applications, the analysis of invariant subspaces and multiplier spaces for spaces of analytic functions of several variables, dilation theory for operator tuples, and extension problems for analytic functions in higher dimensions.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The systematic study of random graphs commenced with the seminal work of Erd" os and Renyi in the 1960s. Beyond the classical connections and synergies between random graphs and computer science, over the last few years a new exciting connection between random graphs and statistical inference has been discovered. These connections have led to important new insights on computational problems and statistical inference problems and to new methods for the analysis of random graphs or random discrete structures in general. In addition, since the late 1990s an insightful approach called the cavity method by physicists has been applied to put forward predictions on structural properties of random graphs and their phase transitions. More recently, it has inspired new algorithms for statistical inference problems such as message passing algorithms and novel spectral algorithms. With this workshop we hope to stimulate research and foster new exciting interdisciplinary collaborations between researchers with different backgrounds and expertise in random graphs, computer science, probability, statistics, statistical inference and information theory.

Probability and Statistics, Game Theory,    Graph Theory and Combinatorics

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop will focus on the results around the classification of algebraic varieties and their sheaves and how they are applied to resolve long standing questions in algebraic geometry.

Algebra,    Geometry and Topology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Systems theory, Control and Automation,    Pattern Recognition and Image Processing, Machine Vision

Georg-August Universität Göttingen

The Summer School is organized by the research group Analysis of PDEs under the umbrella of the newly created DFG funded Research Training Group RTG 2491 Fourier Analysis and Spectral Theory.

The topic of the school is Singular Integral Operators on Nilpotent Lie Groups and Related Topics. In particular, the topics of the advanced courses of the summer school will be: Harmonic Analysis on the Heisenberg Group, PDE on Nilpotent Lie Groups, Restriction Estimates - On Euclidean Space and the Heisenberg Group, and Singular Integral Operators with Flag Kernels.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Group actions are a mathematical approach to analysing structures by studying the rearrangements of the elements of the structure that preserve the defining properties of the structure. Indeed, historically, group theory developed primarily as a technique for handling questions concerning the resolution of algebraic equations (the group introduced here by Galois permutes the roots of the equation), and has since become a standard language for formalising and solving various natural questions from a wide range of mathematics.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

One remarkable development in algebraic number theory over the last two decades is the proof of many cases of the main conjecture of Iwasawa theory for elliptic curves over the rational, leading to spectacular advances on the Birch and Swinnerton-Dyer conjecture. Over the past few years, the methods used to prove these results have been refined to remove some of their hypotheses and extended to other settings, but despite these improvements some important cases remain largely open. This workshop aims to foster new developments in these directions by clarifying the state of the art of the aforementioned results, identifying some of the technical limitations of the current methods, and encouraging the exchange of ideas between participants with different areas of expertise, while also bringing new researchers (recent PhDs and post-docs) in the area up to speed on current methods and results.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematical Sciences Research Institute, Berkeley

This workshop will focus on cutting-edge research in random matrices and integrable probability. We will explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers.

Algebra,    Mathematical Physics

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Despite the enormous commercial potential that quantum computing presents, the existence of large-scale quantum computers also has the potential to destroy current security infrastructures. Post-quantum cryptography aims to develop new security protocols that will remain secure even after powerful quantum computers are built. This workshop focuses on isogeny-based cryptography, one of the most promising areas in post-quantum cryptography. In particular, we will examine the security, feasibility and development of new protocols in isogeny-based cryptography, as well as the intricate and beautiful pure mathematics of the related isogeny graphs and elliptic curve endomorphism rings. To address the goals of both training and research, the program will be comprised of keynote speakers and working group sessions.

Graph Theory and Combinatorics,    Cryptography, Blockchain and Information Security

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The development of high-performance simulation tools for real-life problems involving fluid flows and related transport phenomena frequently requires the use of numerical methods that are high-order accurate in space and time and preserve important physical properties of certain quantities of interest (such as nonnegativity of the water height in shallow water equation models). In recent years, the state of the art in the development of such schemes was significantly advanced by a breakthrough in theoretical analysis which has provided illuminating insights into the properties of existing methods and new design criteria for the development of improved solution strategies. However, many theoretical aspects of physics-aware discretization techniques still require further exploration or have not been put into practice so far. The purpose of this workshop is to bridge the gap between the mathematical theory and engineering practice.

Modeling and Simulation,    Scientific Computing

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematical Sciences Research Institute, Berkeley

The introductory workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Algebra,    Mathematical Physics

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Algebraic techniques have become influential in many areas in theoretical computer science, such as: coding theory, hardness of approximation, communication complexity, learning theory, cryptography, sublinear algorithms, coding theory, communication complexity, social choice theory, and more. The workshop will bring together researchers in these areas, allowing them to learn from each other and facilitate new collaborations.

Information Theory, Foundations of Computer Science,    Software Engineering

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematical Physics,    Astronomy, Astrophysics and Cosmology

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Partial differential equations (PDE) are a rich and deep area of mathematics which is strongly motivated by problems arising in applied sciences and technology, such as physics, engineering, medicine. Most physical phenomena appearing in reality can indeed be modeled through PDE. Unfortunatley, explicit solutions to PDE can only be determined in very few special cases. On the other hand, it is often possible to describe some relevant qualitative and quantitative properties of theirs. This theoretical analysis enables, for instance, to develop effective numerical approximation methods for solutions. The workshop focuses on some fundamental aspects of the theory of PDE, including existence of solutions, their regularity and a priori estimates. Information on these issues allows for a deeper understanding of the structure of solutions and of the physical phenomena that they describe. They will be addressed in connection with some of the most advanced developments of the theory of PDE, that rely upon methods and results from Nonlinear Potential Theory, Harmonic Analysis, Geometric Analysis.

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The geometry of Hyperkahler varieties is certainly one of the most studied topics in Algebraic Geometry, with many connections to Representation Theory and Arithmetic Geometry. The aim of this workshop is to survey the recent developments in this area and to investigate the open problems and conjectures, by creating new collaborations between participants from different research fields.

Algebra,    Geometry and Topology

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

In this workshop our aim is to bring together well-established and early-career researchers from the areas of Analysis of PDEs, Optimal Transport Theory and Geometric Flows to report on their latest contributions and establish new collaborations. The fields of expertise of the participants are broad and will offer a great opportunity for cross-fertilization among diverse communities.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Irregular growth is a ubiquitous phenomenon in nature, from the growth of tumors, crystals, and bacterial colonies to the propagation of forest fires and the spread of water through a porous medium. Mathematical models of random growth have been a driving force in probability theory over the last sixty years and a rich source of important ideas. The analysis of random growth models began in the early 1960s with the introduction of the Eden model by Eden and first-passage percolation by Hammersley and Welsh. The field witnessed several breakthroughs in the 1980s and 1990s, from the introduction of more random growth models, including the Kardar, Parisi, and Zhang (KPZ) equation and the KPZ universality class, to the ground-breaking works of Tracy and Widom and of Baik, Deift, and Johansson, and the seminal works of Newman and coauthors. These results caused a flurry of activity and more analytical and geometrical tools were developed.

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop is dedicated to Hao Wang, for his pioneering work in connecting human and formal thinking that permeates (O1)-(O3). A greater understanding of these topics will no doubt lead to a better understanding of computation in mathematics and computer science, and increase the prominence of mathematical logic and proof theory in China, Asia, and the world.

General Mathematical Research and Multidisciplinary Events,    Mathematical Logic and Foundations

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Recent remarkable advances in learning-based methods are revolutionizing the field of image analysis resulting in a paradigm shift towards data-driven approaches. These methods have already shown tremendous success in a wide range of applications from computer vision such as object detection and object category classifications. To perform efficiently though, such methods typically require a large number of training sample and this requirement is highly impractical or impossible in applications from medical imaging where it is very laborious and expensive to generate labeled data. Another drawback of learning-based method is that they do not come with provable performance guarantees. One remedy to such limitations is to combine data-driven methods with prior knowledge through mathematical and/or physical models in such a way to optimize processing, reconstruction and analysis of medical imaging data without the need of extensive training. This workshop will bring together researchers with a different background ranging from optimization, inverse problem, numerical and harmonic analysis and machine learning to advance state-of-the-art methods combining data- and model-driven approaches for medical imaging.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Advances in data collection and social media have led to network and graph data becoming available in many areas, including social sciences, biological sciences, and engineering. Understanding and modeling network structure, as well as conducting rigorous statistical inference to assess uncertainty, can provide crucial insights into the dynamics and interaction mechanisms of the system. Statistical network analysis to date has largely focused on the setting where a single network is observed as a noisy version of some underlying structure of interest. This setting in itself is challenging, requiring adaptation of existing statistical frameworks to networks and bridging the gap between theoretically optimal performance and computational feasibility. The workshop will start by covering recent advances in this setting.

Probability and Statistics, Game Theory,    Graph Theory and Combinatorics

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Subfactors and vertex operator algebras are mathematical structures that at first glance appear very different, but both are used in the mathematical study of quantum field theory. In particular, vertex operator algebras are algebraic structures arising in two-dimensional conformal field theory (CFT), a quantum field theory with applications ranging from string theory to condensed matter physics to quantum computing. On the other hand, subfactors are closely related to conformal nets, which are a functional-analytic approach to CFT. Because they are both mathematical descriptions the same quantum field theory, the theories of vertex operator algebras and conformal nets are widely believed to be equivalent, but only in the last few years has there been substantial progress in establishing an equivalence. As many important results in conformal field theory have been established for either vertex operator algebras or conformal nets, but not necessarily both, developing connections and equivalences will be useful for answering open questions in both mathematical formulations of CFT.

Mathematical Physics,    Algebra

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop brings together both theoreticians and practitioners from broadly different fields to advance algebraic statistical methodology to data science. While linear algebra underlies classical statistics, in algebraic statistics, the aim is to explore the applicability of nonlinear algebra---which extends algebraic theory beyond linear algebra---to statistical theory. In particular, our goal is to advance the computational feasibility of algebraic statistics. Our focus is specifically on direct applicability of algebraic statistical theory to real datasets. Additionally, this workshop explores other statistical settings that are also algebraic in nature and that find practical applications in various different fields, where nonlinear algebra may also be applied.

Probability and Statistics, Game Theory,    Algebra

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

A key challenge in biology and medicine is to understand how network of interacting genes gives rise to cellular behavior. Experimental limitations and the big data generated by 'omics technologies requires the development of quantitative approaches to overcome this challenge. In the context of mathematical models this challenge takes form of predicting complex dynamic behavior of gene and signaling networks inside cells. Construction of appropriate models is difficult due to large uncertainty in the state of the cell, the efficiency of its enzymes, and the form of interactions between genes.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Locomotion of cells, both individually and collectively, plays an important role in development, the immune response, wound healing, and cancer metastasis. Movement requires force transmission to the environment, and motile cells are robustly-designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission – which ranges from crawling to swimming. The shape and integrity of a cell is determined by its cytoskeleton, and thus the shape changes that may be required to move involve controlled remodeling of the cytoskeleton. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of single cell motility, even in simple cells such as bacteria, is not at hand. At the next level, collective movement requires coordination of these nanomachines, which introduces another level of complexity. This complexity has stimulated mathematical modelling and computational simulations of cell and tissue movement at various levels, which has advanced our understanding of movement on multiple time and space scales.

Modeling and Simulation,    Computational Physics and Numerical Simulation

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Algebra,    Analysis

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

In this workshop, we want to bring together researchers from both sides of this development: those mathematicians specializing in the application of modern algebraic and algebro-geometric methods to the study of algebraic groups and their torsors, as well as those working on relevant aspects of the motivic and cohomological approaches from a more abstract viewpoint. We hope that bringing this mix of researchers together will have a synergistic impact, leading to concrete new applications of the abstract machinery to outstanding problems on quadratic forms, algebras with involution and algebraic groups, but also inspiring progress on the general development of the motivic and cohomological methods.

Algebra,    Group Theory

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Quantum Mechanics and Quantum Information Theory,    Mathematical Physics

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

An aspiration of modern cell biology is to 1) understand how the various cellular components assemble into a cell and 2) understand how cell function arises from the interaction of those components. How do cells form with a specific shape and size? How do they divide and how do cells decide where to divide? How does transport occur in the crowded cellular environment inside a cell? Mathematics has a role in helping answer such questions. Understanding of these phenomena also presents the opportunity to discover new deep mathematical concepts, particularly because it involves chemistry and physics acting across length-scales, from molecules to cells and tissues. BIRS has played a foundational role in the development of what has become known as Mathematical Biology of the Cell, by hosting regular workshops that have helped reveal principles behind how cellular components assemble and organize themselves to form discrete structures, distinct cellular compartments, and form patterns. The underlying goal of this meeting of interdisciplinary and diverse scientists is to understand the fundamental principles connecting cell signaling, geometry, transport, and mechanics.

Molecular Biology,    Biophysics, Medical Physics

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Convex geometry and partial differential equations are two important mathematical branches. A constantly growing interaction between them in the last decades has resulted in significant progress in both areas. The goal is to solve questions in analysis, by combining the (affine) geometry of convex bodies and methods from partial differential equations, in particular, Monge-Ampere type equations. First major results include affine inequalities that are stronger than their Euclidean counterparts. Applications appear in information theory, probability theory and stochastic geometry.

Geometry and Topology,    Calculus, Differential Equations and Integration

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Understanding the real solutions of polynomials or systems of polynomial equations is at the heart of many problems both in the realm of pure mathematics and in the mathematical modeling of networks in systems biology, in computer aided geometric design, or in the control of mechanisms. While there exist a lot of celebrated results (for example, bounds exploiting the signs of the coefficients of a univariate polynomial or bounds taking into account the number of terms), even some basic questions are still unsolved. There has been a recent explosion of activity in this area, where different tools have started to be connected in new and unexpected ways, such as tools from the theory of matroids, from fewnomial theory, or from convex algebraic geometry. This workshop will bring together experts from close but different areas in real algebraic geometry to collaborate and will lead to further progress (both theoretical and practical) on a number of problems on the real solutions of polynomials. Specific consideration is given on the problem of counting and bounding the number of real roots as well as on questions of stability.

Analysis,    Modeling and Simulation

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

An outstanding problem of modern physics is the reconciliation of the two most successful broad theories of physics: general relativity, which describes the gravitational force exerted by massive objects in terms of the bending and rippling of spacetime, and quantum mechanics, which describes the behavior of matter on the minute scales of subatomic particles such as electrons. While both theories are remarkably successful independently, they appear to give contradictory predictions of phenomena that involve gravity at the small scales at which quantum mechanics is relevant. Such phenomena include the Big Bang, when the universe was small enough to be described by quantum mechanics and sufficiently dense to also require a gravitational description; also the process of the final stages of the death of a large star, when a black hole is formed and the star’s matter is concentrated in an extremely small volume. A proper description of these phenomena requires a unified theory of quantum gravity.

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Present day biology generates a wealth of data from which tumor biology and tumor evolution can be inferred, and therapeutic strategies can be developed. Most clinical (and research) samples are comprised of a mixture of different cells, including multiple different populations of cancer cells (‘subclones’) and a variety of normal cell types. Effective use of these data thus requires data from individual cell types to be deconvolved. A number of subfields are independently developing mathematical and statistical deconvolution techniques. While at first glance these subfields are largely disparate, there are clear opportunities for synergies to be developed. This workshop will fill this gap by bringing together researchers from several of these fragmented subfields across a wide range of backgrounds (computational biology, mathematics, statistics, computer science, biomedicine, etc.) to provide a synergistic forum for cross-disciplinary learning, discussion and collaboration.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The incredible advances in artificial intelligence applied to images need to be combined with geometric tools to be applied in higher dimensional data and for applications to 3D objects, such as those in Augmented Reality, Virtual Reality environments, data from sensors of self-driving cars, computational anatomy, and other domains of technological applications. In this workshop we will bring together experts from academia, government stakeholders, applied researchers from industry, as well as graduate students and early career scientist to interact and develop novel solutions that apply abstract tools from high dimensional geometry to contribute to the solution of these problems.

CIRM – Centre International de Rencontres Mathématiques

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Nonlinear inverse problems are ubiquitous in medical sciences, engineering, physics and other natural sciences. This workshop will advance a statistical paradigm that allows underpinning statistical decision making in such problems in a scientifically rigorous way. This will be achieved by providing `frequentist' large sample guarantees for inferences arising from commonly used (Bayesian or non-Bayesian) algorithms in such problems. Thereby, a large cluster of applied problems, where algorithms are used for day-to-day decision making with statistical data, will be put on a solid and robust foundation, facilitating its confident use in modern society.

Algebra,    Probability and Statistics, Game Theory

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Stability theory, in the sense of mathematical logic, consists of a collection of technical methods first developed to address the logical problem of classifying abstract models of mathematical theories. Stability theory has proven to be applicable to other mathematical problems such as understanding rational solutions of algebraic equations. It has recently been shown that the techniques and methods used for the classification described above can be used in much more general settings with applications to other areas of mathematics such as algebraic geometry, additive combinatorics and extremal graph theory. Researchers at this meeting will study these developments to deepen these applications, and to extend the scope of stability theory to an even wider range of mathematical theories.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The information that determines our genetic make-up – from our eye color to our propensity to get cancer or genetic diseases – is encoded in the DNA sequence of our genomes. This DNA information is interpreted by proteins called transcription factors that ‘read’ the four-letter code in our DNA, promoting the activation or repression of genetic programs. Unfortunately, we have been unable to decipher the non-protein-coding portion of our genomes, which comprises >95% of our DNA, even though we now have access to thousands of fully sequenced human genomes and the numbers are increasing daily. A fundamental problem of modern biology will be how to discern DNA differences between people that affect our physical differences and the manifestation of disease. As a result, a major challenge facing computational and structural biologists is to crack the DNA code that will allow us to understand the impact of DNA differences on protein-DNA interactions and gene expression. The solution to this challenge will likely come from the convergence of theoretical, computational, biophysical, and structural approaches. The BIRS format is ideal for bringing together this combination of scientists in an informal and collaborative setting to further advance this goal.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Our workshop aims at bringing together established and young mathematicians working in complex analytic, differential and symplectic geometry, as well as in geometric PDE's, in an attempt to produce a road-map for future research in the domain of LCS manifold. By focussing during a single week on the topological, differential geometric and complex analytic aspects of the theory of locally symplectic manifolds, we hope to provide the necessary synergy for a substantial future progress in the field. A problem session will be organized at the end of the workshop.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

In this workshop, experts in the physics and mathematics of string theory shall gather together to discuss the current progress on the study of the physical consequences (for particle physics and cosmology) of string models, and to explore new exciting formal (and informal) proposals that may constitute important tools to gain a better understanding of string theory and its possible predictions. Besides traditional overview talks and seminars on the ongoing research in this field, the workshop will provide an adequate environment for fruitful discussion and collaboration.

Conventional and Renewable Energy Production,    Mathematical Physics

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Graph Theory and Combinatorics,    Operational research

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The Functoriality conjectures, formulated by Langlands in 1967, have been a driving force behind much of the work in both Number theory and Representation theory in the last 50 years. This workshop will explore a relatively new approach to the conjectures stemming from Langlands' recent proposal called ``Beyond Endoscopy''. This proposal has since blossomed in the work of many mathematicians and has produced very interesting recent results in several areas of mathematics from algebraic geometry through representation theory to analytic number theory.

Number Theory, Arithmetic,    Algebra

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Gravitational-waves are a new way to explore the sky and uncover the Universe’s deepest mysteries. Although the first detection of these "ripples of space-time" is only a few years old, scientists can now harness the potential of gravitational waves in testing Einstein’s General Relativity theory under extreme conditions, helping to understand the origin of matter, and measuring the evolution of the Universe. Researchers from all around the world are gathering in Oaxaca to discuss recent progress in, and the future of gravitational-wave science. The workshop "Detection and analysis of gravitational waves in the era of multi-messenger astronomy: From mathematical modelling to machine learning", provides a forum, unique in its genre, for discussing new mathematical methods in modelling, detecting, and analyzing gravitational waves, as well as their integration with machine learning, or artificial intelligence.

Astronomy, Astrophysics and Cosmology,    High Energy Physics, Particles and Fields

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Graphs are the standard mathematical model of many real-world entities: computer networks, road and highway networks, drainage systems, river networks, electrical networks, and so on. In some cases, these highly-complicated graphs are contained in the product of two or more much simpler graphs. In a recent breakthrough, it was shown that this is the case for planar or near-planar graphs like those that model river, road, and highway networks; any such graph is contained in the product of a simple tree-like graph and a path. This product structure gives deep insight into these graphs and their properties, allowing a host of mathematical and algorithmic tools to be applied to these graphs. The goal of this workshop is to continue the search for product structure in more general classes of graphs as well as to find new methods to exploit such product structure mathematically and algorithmically, when it is present.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The workshop focuses on the novel mathematical challenges of statistics and machine learning. The spectacular success of machine learning in a wide range of applications opens many exciting theoretical challenges in a number of mathematical fields, including probability, statistics, combinatorics, optimization, and geometry. BIRS will bring together researchers of machine learning and mathematical statistics to discuss these problems. The principal topics include combinatorial statistics, online learning, and deep neural networks.

Neural Networks and Artificial Intelligence, Machine Learning,    Pattern Recognition and Image Processing, Machine Vision

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The aim of this workshop is to bring together researchers working on objective Bayesian methodology, nonparametric Bayesian methods and machine learning. Objective Bayesian methods are evolving from a historically narrower focus on issues related to prior specification to research themes that are more broadly related to default methods in Bayesian statistical analysis. This naturally leads to an increasing overlap with Bayesian nonparametric modeling and machine learning. The workshop seeks to exploit this increasing intersection by bringing together participants from all three research communities.

Probability and Statistics, Game Theory,    Software Agents and Intelligent Agents in Artificial Intelligence

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

CIRM – Centre International de Rencontres Mathématiques

CIRM-IHP PROGRAM - RESEARCH SCHOOL

MRSI – Mathematical Sciences Research Institute, Berkeley

Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond. Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics.

Complex Systems, Chaos and Self-Organisation,    General Mathematical Research and Multidisciplinary Events

CIRM – Centre International de Rencontres Mathématiques

MULTIYEAR PROGRAM - RESEARCH SCHOOL

CIRM – Centre International de Rencontres Mathématiques

MULTIYEAR PROGRAM - RESEARCH SCHOOL

CIRM – Centre International de Rencontres Mathématiques

RESEARCH SCHOOL

Information Theory, Foundations of Computer Science,    Training in Computer Science, Courses

CIRM – Centre International de Rencontres Mathématiques

RESEARCH SCHOOL