Courses and Events for Math Students and Early Career Researchers

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

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Algebra,    Geometry and Topology

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

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

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

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

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

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

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

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

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

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

Mathematical Physics,    Thermodynamics, Fluid Dynamics and Statistical Physics

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

Geometry and Topology,    Group Theory

CIRM – Centre International de Rencontres Mathématiques

MULTIYEAR PROGRAM - RESEARCH SCHOOL

The Southeastern Analysis Meeting (SEAM) promotes interaction between researchers and encourages research and education in the field of analysis. The meeting has a rich history and its main purpose is to bring together experienced researchers, junior faculty, and graduate students to discuss recent work and advances in Operator Theory, Classical Complex Analysis, Harmonic Analysis, Function Theoretic Operator Theory, and related areas.

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

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

Analysis,    Thermodynamics, Fluid Dynamics and Statistical Physics

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

Neural Networks and Artificial Intelligence, Machine Learning,    Natural Language Processing, Computational Linguistics

IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

The program opens with four days of tutorials that will provide an introduction to major themes of the entire program and the four workshops. The goal is to build a foundation for the participants of this program who have diverse scientific backgrounds. For those participating in the long program, please plan to attend Opening Day on March 7, 2022 as well. Others may participate in Opening Day by invitation from the organizing committee.

Part of the Long Program Advancing Quantum Mechanics with Mathematics and Statistics

Courses and Events for Physics Students,    Quantum Mechanics and Quantum Information Theory

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

Quantum Mechanics and Quantum Information Theory,    Information Theory, Foundations of Computer Science

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

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

Information Theory, Foundations of Computer Science,    Events for IT Students and Early Career Researchers

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

Applied Mathematics (in general),    Probability and Statistics, Game Theory

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

CIRM – Centre International de Rencontres Mathématiques

MULTIYEAR PROGRAM - RESEARCH SCHOOL

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

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

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

IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

This workshop will set the stage and define research directions for the rest of the program. The idea is to achieve a healthy mix between researchers developing quantum theories and methods on different spatial and temporal scales, providing a forum to discuss the advances in multiscale modeling in quantum mechanics and pave the way to stronger coupling between existing methods and completely novel quantum approaches. The main question is how to integrate already existing quantum methods to reduce their weaknesses, improve their applicability, and enable quantum calculations on much larger scales? For example, electronic orbitals obtained from density-functional theory calculations are being increasingly used to compute correlation energies using many-body Green’s function theories and explicitly correlated methods. Such synergies provide a way to approach the exact solution of the Schroedinger equation, in addition to significantly accelerating the cost of explicit many-body calculations. On a much larger spatial scales, multiscale coupling of approximate many body Hamiltonians with Maxwell’s equations allows to unify microscopic and continuum treatments of van der Waals and Casimir interactions, eventually making it possible to push the boundaries of such calculations to macroscopic systems.

Courses and Events for Physics Students,    Quantum Mechanics and Quantum Information Theory

Orthodox Academy of Crete

UNILOG is a series of world events. Since the first edition in 2005 in Montreux, Switzerland, it has gathered many famous researchers: Saul Kripke, Jaakko Hintikka, Yuri Gurevich, Rohit Parikh, Michael Dunn, Dov Gabbay, Wilfrid Hodges, Hartry Field, Pierre Cartier, Krister Segerberg, Melvin Fitting, Gerhrad Jaeger, Hiroakira Ono, Daniele Mundici, Jan Wolenski, Patrick Blackburn, John Corcoran, Heinrich Wansing, David Makinson, Newton da Costa, Peter Schroeder Heister, Göran Sundholm, Didier Dubois, Arnon Avron, Volker Peckhaus, Graham Priest, Benedikt Löwe, Stepen Read, Gila Sher, Jonathan Seldin, Sun-Joo Shin, Bruno Poizat, Sara Negri, Ahti-Veikko Pietarinen, Valentin Goranko, Yde Venema, Jouko Väänänen and more ... UNILOG promotes logic in all its aspects: mathematical, philosophical, computational, semiological, historical, and the relation between logic and other fields: physics, biology, economics, law, politics, religion, music, literature, pedagogy, color theory, medicine, psychology, psychoanalysis, cognitive science, architecture, artificial intelligence, sociology, linguistics, anthropology. UNILOG is a combination of a congress and a school. There is also a secret speaker and the world logic prizes contest.

Hausdorff Center for Mathematics

A large number of real-life phenomena - spread through chemistry, ecology, and biology - can be mathematically described through diffusive systems such as reaction-diffusion systems with linear or nonlinear diffusion, nonlocal diffusion, and cross-diffusion systems. These systems are extremely interesting to investigate not only due to their importance in applications (reaction chemistry, population dynamics, collective phenomena in life sciences) but also because they give rise to a rich variety of complex behaviours, such as pattern formation and bifurcations. In the second edition of this School – which follows the 2021 online first edition – we aim to bring together experts from different communities to cover the investigation of diffusive systems from several viewpoints: analytically, combining methods and techniques from Partial Differential Equations (PDEs) and dynamical systems to derive and analyse mathematical models for the applied phenomena; numerically, reviewing the most recent techniques and software for the computation of bifurcation diagrams and continuation with respect to the systems’ parameters; and, last but not least, from the applied - in particular biological – viewpoint, since a constant exchange of knowledge between the theoretical investigations and the experimental data is crucial in advancing research in this area.

The Copenhagen School of Stochastic Programming is a PhD course that provides a rigorous and research-oriented introduction to stochastic programming, a mathematical framework for decision-making in the presence of uncertainty. In many real-life problems, important information is unknown to the decision-maker and only distributional information is available. Examples include the scheduling of power generation while demand and renewable production is uncertain, investments in assets with uncertain future returns or production of goods for which demand is stochastic.

It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem (the basic mechanism being to add nominals --- atomic symbols true at a unique point --- together with extra modalities to exploit them) often actually improves the behaviour of the underlying modal formalism. For example, it becomes far simpler to formulate modal tableau systems, resolution, and natural deduction in hybrid logic, and completeness results can be proved of a generality that is simply not available in ordinary modal logic. That is, hybridization --- adding nominals and related apparatus --- seems a reliable way of curing many known weaknesses in ordinary modal logic.

This workshop is devoted to exploring connections between non-classical logics and the rational use of defective information in the sciences, as well as the inferential practices in the sciences—particularly, those which make use of defective information.

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

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

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

Analysis,    Numerical Analysis and Computational Mathematics

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

Algebra,    Scientific Computing

IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

The first one is the rigorous mathematical derivation of reduced models from reference quantum models in some regimes such as the semiclassical limit, adiabatic limit, thermodynamic limit, and high/low density limit. New approaches have been developed in the past two decades, which lead to successful mathematical derivations of reduced models in a number of settings. However, in many settings the mathematical relations between reference and reduced models and the domain of validity of the latter still have to be clarified. The second aspect is concerned with effective interactions. Interactions between elementary particles typically have very simple functional form such as the Coulomb potential between two charged particles. However, upon solving the many-particle quantum mechanical equations, complex and intricate interactions emerge. The understanding and systematization of such interactions between composite objects provides a pathway to better understand quantum mechanics itself and constitutes the basis for developing coarse-grained approaches to describe interactions in large quantum systems. The third aspect is about simplified quasiparticle or collective mode descriptions of complicated quantum states, using one-particle spin-orbitals, plasmons, phonons, polarons, or excitons. Such objects are embedded in finite or infinite dimensional Hilbert spaces defined by the basis set utilized to expand the many-body wavefunction. Recently, many interesting efforts have been dedicated to analyzing and visualizing quantum states in Hilbert spaces, as well as to map and embed Hilbert spaces between different quantum systems. Such mapping and embedding of Hilbert spaces brings out novel insights into the intricate nature of quantum fluctuations and should ultimately allow to develop better and more reliable approximations for solving complex quantum systems.

Courses and Events for Physics Students,    Quantum Mechanics and Quantum Information Theory

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

Algebra,    Analysis

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

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

Neural Networks and Artificial Intelligence, Machine Learning,    Systems Biology and Computational Biology

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

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

Graph Theory and Combinatorics,    Probability and Statistics, Game Theory

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

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

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

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

Algebra,    Analysis

IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

Simulating very large quantum systems require new numerical methods and algorithms. Such simulations indeed lead to solving linear and nonlinear systems of equations and eigenvalue problems, that are characterized by high dimensionality, large ranks (for tensor problems), and extreme scale. They must exploit massive parallelism in both space and time and rank-reduction methods, through deterministic or stochastic approaches, optimized data structures, and minimize communication. It is also key to have tools at hands to assess the quality of the simulation results. Error analysis is of major relevance in the simulation of quantum systems, but to date, it has received less attention than in other fields such as fluid or structure dynamics. The error between the exact and computed values of a given physical quantity of interest (QOI), e.g. the dissociation energy of a molecule, has several origins: a model error (resulting from the choice of a computationally tractable, but not extremely accurate, model, e.g. Kohn-Sham with B3LYP functional), a discretization error (resulting from the choice of a finite basis set), an algorithmic error (due to the choice of stopping criteria in Self-Consistent Field and other iterative algorithms), an implementation error (due to possible bugs or uncontrolled round-off errors), a computing error (due to random hardware failures). Quantifying these different sources of errors is key for two reasons. First, guaranteed estimates on these five components of the error would allow one to supplement the computed value of the QOI returned by the numerical simulation with guaranteed error bars (certification of the result). Second, this would allow one to choose the parameters of the simulation (approximate model, discretization parameters, algorithm and stopping criteria, data structures?) in an optimal way in order to minimize the computational effort required to reach the target accuracy (error balancing). Since molecular simulation consumes a massive amount of CPU time in scientific research centers worldwide, this would have a major impact on the use of scientific computing resources.

Courses and Events for Physics Students,    Quantum Mechanics and Quantum Information Theory

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

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

Analysis,    Calculus, Differential Equations and Integration

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

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

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

The Institute for Computational and Experimental Research in Mathematics (ICERM)

With the substantial recent progress in connectomics, the study of comprehensive maps of nervous systems, much more is known about the connectivity structure of brains. This has led to a multitude of new questions about the relationship between connectivity patterns, neural dynamics and brain function, many of which lead to new mathematical problems in graph theory and dynamics on graphs. The goal of this workshop is to bring together a broad range of researchers from neuroscience, physics, mathematics, and computer science to discuss new challenges in this emergent field and promote new collaborations.

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

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

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

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

Probability and Statistics, Game Theory,    Operational research

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

Probability and Statistics, Game Theory,    Calculus, Differential Equations and Integration

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

CIRM – Centre International de Rencontres Mathématiques

RESEARCH SCHOOL

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

IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

Quantum mechanics has strong connections with probability theory and statistics. Quantum states are amenable to probabilistic interpretation based on laws of statistics. Many quantum problems can be reformulated in terms of Feynman’s path integral formulation, which amounts to computing quantum partition functions using statistical sampling techniques. In addition, new statistical learning approaches are emerging that aim to incorporate “quantumness” to ensure unitarity and long-range correlations that are so ubiquitous in quantum systems. Considering these recent developments, it appears timely to bring together the large community of people working on quantum systems and statistical techniques. This workshop will broadly address the reaches and limitations of statistics as applied to the modeling and understanding of quantum systems and highlight examples where quantum and statistical models enhance each other.

Courses and Events for Physics Students,    Quantum Mechanics and Quantum Information Theory

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

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

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

CIRM – Centre International de Rencontres Mathématiques

RESEARCH SCHOOL

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

Graph Theory and Combinatorics,    Algorithms and Data Structures

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

Group Theory,    Algebra

Mathematical Sciences Research Institute (MRSI)

The field of Integral Equations has a long and distinguished history, being the driving force behind many fundamental developments in various areas of mathematics including Harmonic Analysis, Partial Differential Equations, Potential Theory, Scattering Theory, Functional Analysis, Complex Analysis, Operator Theory, Mathematical Physics and Numerical Analysis.

Calculus, Differential Equations and Integration,    Applied Mathematics (in general)

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

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

Institut de Recherche Mathématique Avancée de Strasbourg

The aim of the summer school is to provide an introduction to recent advances in the understanding of the number-theoretic content of the cohomology of arithmetic groups and of algebraic K-groups of number rings. Uncovering this information reveals deep connections with algebraic geometry, namely with the theory of motives and with motivic homotopy theory. Surprisingly, this happens even when the arithmetic groups under consideration are not directly linked with algebraic varieties.

Mixed Tate motives, Dedekind zeta values, and polylogarithms, Weighted cohomology of Shimura varieties, Hermitian K-theory of number rings and special values of L-functions, Motivic cohomology and cohomology of arithmetic groups

Algebra,    Number Theory, Arithmetic

Mathematical Sciences Research Institute (MRSI)

The MSRI Undergraduate Program (MSRI--UP) is a comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.

Systems Biology and Computational Biology,    Genomics and Bioinformatics

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

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

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

Analysis,    Numerical Analysis and Computational Mathematics

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

Lake Como School of Advanced Studies

Probability and Statistics, Game Theory,    Complex Systems, Chaos and Self-Organisation

Lake Como School of Advanced Studies

In the scientific community a growing interest arises on the mathematical formulation and study of evolution systems stemming from Biology and Health Sciences, focusing in particular on tumor growth models, bio-materials and complex systems. This subject turns out to be particularly significant for Mathematical Biology especially during these years, in which a joint venture of the European Mathematical Society (EMS) and the European Society for Mathematical and Theoretical Biology (ESMTB) started. It results that applications of Mathematics in Bio-medical sciences are completely opening new pathways of interactions and they constitute a huge source of new mathematical problems. The school aims to gather well-known experts in modeling of Bio-medical systems and mathematicians directing their research to the analysis of qualitative properties of solutions of the related partial differential equations and their implication on the biological behaviour. The main objective is to attract students interested in mathematical modeling and analysis in applied sciences.

Mathematical Sciences Research Institute (MRSI)

Representation Theory has undergone a revolution in recent years, with the development of what is now known as higher representation theory. In particular, the notion of categorification has led to the resolution of many problems previously considered to be intractable. The school will begin by providing students with a brief but thorough introduction to what could be termed the “bread and butter of modern representation theory”, i.e., compact Lie groups and their representation theory; character theory; structure theory of algebraic groups. We will then continue on to a number of more specialized topics. The final mix will depend on discussions with the prospective lecturers.

Algebra,    Group Theory

Mathematical Sciences Research Institute (MRSI) and the FORTH-IACM Institute in Crete

This summer graduate school is a collaboration between MSRI and the FORTH-IACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations. This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the Mean curvature flow and other fully non-linear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.

Analysis,    Geometry and Topology

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

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

Applied Mathematics (in general),    Scientific Computing

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

Centre de Recerca Matemàtica (CRM), Barcelona

The JISD is an annual meeting between experts and young researchers in Dynamical Systems and Partial Differential Equations (PDEs). It is designed to encourage and enhance exchange of knowledge and methods, with the goal of advancing the study of cutting edge problems in the aforesaid fields of mathematics and with the aim of fostering the interaction among the participants. The symposium is aimed at local researchers, as well as scientists from the rest of Spain and foreign countries. It is organized into four advanced courses of about 7 hours and complemented by a poster session by young researchers. Throughout the latest editions the attendance numbers have ranged between 60 and 100 participants, mostly internationals.

Email: nhernandez@crm.cat

Dynamical systems, PDEs

General Mathematical Research and Multidisciplinary Events,    Calculus, Differential Equations and Integration

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

Algebra,    Geometry and Topology

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

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

Analysis,    Calculus, Differential Equations and Integration

Mathematical Sciences Research Institute (MRSI)

The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many real-world networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi. Spurred by these findings, many novel models have been introduced and properties have been investigated.

Graph Theory and Combinatorics,    Complex Networks

Mathematical Sciences Research Institute (MRSI)

Algebra,    Calculus, Differential Equations and Integration

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

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

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

Geometry and Topology,    Algebra

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

The Institute for Computational and Experimental Research in Mathematics (ICERM)

At the ICERM workshop "Lean for the Curious Mathematician 2022", experts in the Lean theorem prover will explain how to do number theory, topology, geometry, analysis, and algebra in the Lean theorem prover. This will be accessible to mathematicians without a specific background in computer-proof systems. The material covered will range from undergraduate mathematics to modern research. Participants will be invited to begin formalizing mathematical objects from their own research.

University of Colorado Boulder

The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. This will be a problem set focused summer school surrounding four mini-courses.

1) Fixed point theory and Nielsen theory 2) Categorical Approach to Duality 3) Spectra 4) Trace Methods

Pacific Institute for the Mathematical Sciences

The two-week summer school will be valuable for students learning homotopy theory, symplectic geometry, and applications of Floer theory to low-dimensional topology. One goal of the summer school is to increase the number of researchers familiar with the techniques and problems in both modern homotopy theory and symplectic geometry, but the school will also be useful to students interested only in homotopy theory or only in Floer theory.

Mathematical Sciences Research Institute (MRSI)

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Algebra,    Geometry and Topology

Mathematical Sciences Research Institute (MRSI) and University of Oxford

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

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

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

ICMS, Edinburgh

The Young Researchers in Combinatorics workshop is aimed at PhD students and early-career academics working in Extremal and Probabilistic Combinatorics and related fields. By building an environment of mostly young researchers, we hope the participants will feel free to contribute their ideas openly, thus preparing them to undertake their own research projects. The workshop will consist mostly of working sessions in which participants collaborate on research problems, and a limited number of talks and lectures.

Learning theory is a rich field at the intersection of statistics, probability, computer science, and optimization. Over the last decades the statistical learning approach has been successfully applied to many problems of great interest, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. These impressive successes relied crucially on the mathematical foundation of statistical learning.

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.

Analysis,    Mathematical Physics

The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.

Number Theory, Arithmetic,    Numerical Analysis and Computational Mathematics

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

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

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

Algebra,    Calculus, Differential Equations and Integration

Mathematical Sciences Research Institute (MRSI)

The summer school will lead participants from appealing, simple-to-state problems at confluence of combinatorics, geometry, and topology to sophisticated topological methods that are required for their resolution. In recent years topological methods have found numerous novel applications in mathematics and beyond, such as in data science, machine learning, economics, the social sciences, and biology. The problems we will discuss are particularly well-suited to rapidly put students in a position to approach related research questions.

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

Analysis,    Applied Mathematics (in general)

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

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

BIRS - Banff International Research Station

The summer school will give a self-contained introduction aimed at beginning graduate students, and introduce participants to the latest developments. In addition to attending the lectures, students will meet in intensive problem and discussion sessions that will explore and extend the topics developed in the lectures.

Geometry and Topology,    Graph Theory and Combinatorics

Mathematical Sciences Research Institute (MRSI)

The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory.

Geometry and Topology,    Algebra

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

Applied Mathematics (in general),    Systems Biology and Computational Biology

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

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

Graph Theory and Combinatorics,    Geometry and Topology

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

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

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

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

The mathematics and physics around gauge theory have, since their first interaction in the mid 1970's, prompted tremendous developments in both mathematics and physics. Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories. This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology. Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications. The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.

Mathematical Physics,    Computational Physics and Numerical Simulation

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

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

CIRM – Centre International de Rencontres Mathématiques

Neural Networks and Artificial Intelligence, Machine Learning,    Natural Language Processing, Computational Linguistics

Erdős Center, Rényi Institute

The theory of automorphic forms is a central area of modern mathematics due to its depth and connections to a large number of other disciplines. This feature makes it attractive but also difficult to enter. The summer school will provide a motivated introduction to this rich field through exciting recent developments. It is aimed at graduate students and early career researchers. Four minicourses will be given by top researchers of the younger generation. Financial support will be provided to selected participants in the form of accommodation and catering (details to be shared later).

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

Probability and Statistics, Game Theory,    Graph Theory and Combinatorics

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

CIRM – Centre International de Rencontres Mathématiques

Probability and Statistics, Game Theory,    Scientific Computing

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

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

Algebra,    Geometry and Topology

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

Lake Como School of Advanced Studies

Mathematical Sciences Research Institute (MRSI)

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

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

Applied Mathematics (in general),    Applied Physics (general)

Lake Como School of Advanced Studies

Neural Networks and Artificial Intelligence, Machine Learning,    Software Agents and Intelligent Agents in Artificial Intelligence

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

Numerical Analysis and Computational Mathematics,    Mathematical Physics

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

Algebra,    Geometry and Topology

Lake Como School of Advanced Studies

Probability and Statistics, Game Theory,    Modeling and Simulation

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

Applied Mathematics (in general),    Modeling and Simulation

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

Algebra,    Geometry and Topology

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

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

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

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

Numerical Analysis and Computational Mathematics,    Analysis

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

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

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

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

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

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

Applied Mathematics (in general),    Geophysics and Geology

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

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

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

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

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)

Mathematical Sciences Research Institute (MRSI)

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.