Conférences - Géométrie et topologie

Birational geometry is a classical mathematic subject dating back to the late 1800s. It aims to classify geometric shapes by looking at the majority of their points and asks "if I remove some points from shape A and some other points from shape B, do they become the same shape?". This turns out to be a surprisingly difficult and fundamental mathematical question. Perhaps more surprising is that the classification of geometric shapes from birational geometry is related to the classification of abstract mathematical gadgets called derived categories, a formal language developed by prominent mathematicians in France in the 1960s. However, the relationship between derived categories and birational geometry remains unproven.

BIRS-affiliated mathematics research centre, Casa Matemática Oaxaca (CMO)

Valuation theory grew out of integral geometry, and studies such geometric quantities as volume, surface area, and their generalizations. Spaces with curvature bounds are geometric objects which are not necessarily smooth, but that retain nevertheless some of the features of smooth spaces. For example convexity/concavity properties of the distance function can be seen as a non-smooth generalization of the smooth notion of curvature of constant sign.

Centre International de Rencontres Mathématiques (CIRM)

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

Cours et évènements pour étudiants en mathématiques,    Théorie des graphes et combinatoire

The possibility of using quantum mechanics to build computers that are both faster and more secure is an exciting technological leap. One of the most promising pathways to a robust architecture, referred to as topological quantum computing, has lead to fascinating research at the frontier of mathematics and physics. Properties of new, exotic states of matter can be understood - and hence implemented in practice - using tools that were developed by pure mathematicians in connection to surfaces and their curvature. This workshop is bringing together international experts to explore the intimate connections between such topological properties of quantum matter and the key resource of quantum computing: entanglement.

Centre International de Rencontres Mathématiques (CIRM)

Mathematical Sciences Research Institute (MSRI)

The study of discrete subgroups of Lie groups and the associated locally symmetric manifolds has a long and rich history, with powerful interconnections between the geometry of the locally symmetric space, topology of towers of its finite covers, and number-theoretic aspects. More recently dynamical and probabilistic techniques have been fruitfully employed to study these groups and spaces. The workshop will take stock of recent developments in these highly active fields from a variety of backgrounds.

Georgia Institute of Technology, Department of Mathematics

This will be the tenth annual Tech Topology Conference, but the first held online. There will be seven invited speakers, and participants are welcome to sign up to give lightning talks (which are only five minutes long). The deadline to submit a proposal for a lightning talk is October 23rd. There will also be opportunities to socialize, and meet fellow topologists even with the online format.

topology

American Institute of Mathematics, San Jose, California

This workshop, sponsored by AIM and the NSF, will bring together mathematicians from a variety of backgrounds to discuss a central problem in mirror symmetry: the existence of special Lagrangian submanifolds, and their holomorphic mirrors, stable vector bundles. These two classes of objects form a set of canonical geometric objects, described by fully nonlinear partial differential equations (PDEs), which play a central role in mirror symmetry. Dating back to work of Thomas-Yau, it has long been conjectured that the existence of solutions to these nonlinear PDEs is equivalent to a purely algebraic notion of stability. This conjectural picture connects diverse fields of mathematics, ranging from stability conditions on derived categories, to symplectic geometry and the Fukaya category, to the study of the Lagrangian mean curvature flow and fully nonlinear systems of PDEs.

The central topics for the workshop are: The Lagrangian Mean Curvature Flow, singularity analysis, and connections with the Fukaya category. The deformed Hermitian-Yang-Mills equation, infinite dimensional GIT, and fully nonlinear systems. Understanding the Thomas-Yau conjecture for toric Fano manifolds and Landau-Ginzburg models.

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

Cours et évènements pour étudiants en mathématiques,    Algèbre

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.

Théorie des groupes,    Cours et évènements pour étudiants en mathématiques

ICERM

This introductory workshop in combinatorial algebraic geometry is aimed at early career mathematicians and other mathematicians looking for an entry point into the field. The workshop will feature expository lectures on some of the basic objects of interest, together with "expert'' lectures discussing some current trends in the field. There will also be ample time for problem sessions and discussions.

Tél.: [4018635796];     Email.: teresa.fitzsenry@icerm.brown.edu

Algèbre,    Cours et évènements pour étudiants en mathématiques

ICERM

Research in combinatorial algebraic geometry utilizes combinatorial techniques to answer questions about geometry. Typical examples include predictions about singularities, construction of degenerations, and computation of geometric invariants such as Gromov-Witten invariants, Euler characteristics, the number of points in intersections, multiplicities, genera, and many more. The study of positivity properties of geometric invariants is one of the driving forces behind the interplay between geometry and combinatorics. Flag manifolds and Schubert calculus are particularly rich sources of invariants with positivity properties.

Tél.: [4018635030];     Email.: info@icerm.brown.edu

ICERM

This workshop will focus on the development of software to facilitate research in combinatorial algebraic geometry, based on the SAGE Mathematical Software System and the OSCAR Computer Algebra System. Special attention will be given to efficient computations with multi-variate polynomials, which is a critical part of many algorithms in combinatorial algebraic geometry. Aside from development of software, the workshop will feature a series of talks about polynomial computations, as well as introductory lectures about Sage and Oscar.

Email.: info@icerm.brown.edu

Algèbre,    Théorie des graphes et combinatoire

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

This workshop will have a special focus on control theory and control systems. Control theory deals with the problem of shaping the behavior of ``systems,'' where a system can be an engineered object, such as a robot or a train, or a natural one, such as a flock of birds or even the brain. The basic driving questions are how to actuate, and how to design, the system to get it to perform as desired. Due to the wide variety of physical systems that control theory handles, the use of more abstract mathematical tools is very well suited to this field, and has already proven useful many instances, such as the study of system stability or optimal design of control system.

Systèmes, contrôle et automatisation,    Mathématiques appliquées (en général)

The Fields Institute

This workshop will showcase recent advances in combinatorial and geometric rigidity theory. Particular topics of interest include d-dimensional rigidity, global and universal rigidity, symmetry and periodicity, rigidity of alternate constraint systems and applications..

Algèbre,    Théorie des graphes et combinatoire

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.

Cours et évènements pour étudiants en mathématiques,    Statistique, Théorie des jeux

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.

Cours et évènements pour étudiants en mathématiques,    Physique des hautes énergies, des particules et des champs

This workshop, sponsored by AIM and the NSF, will be devoted to exploration of the recently discovered connections between conformal sympathetic structures, contact topology and the theory of codimension one foliations.

ICERM

The purpose of the workshop is to bring together a diverse group of researchers working on combinatorial and geometric aspects related to spaces with symmetries. The workshop will cover problems arising from various flavors of Schubert Calculus and enumerative geometry on flag manifolds, and problems from geometric representation theory and combinatorial Hodge theory. The topics covered include the study of Littlewood-Richardson coefficients, quantum cohomology and quantum K theory of flag manifolds, Maulik-Okounkov stable envelopes and characteristic classes, conformal blocks, and combinatorics related to moduli spaces, Macdonald theory, and quiver polynomials, Soergel bimodules, Hodge theory of matroids. These are trends in a rapidly developing area, and our aim is to facilitate interactions among researchers who work on different problems but employ similar techniques, at the intersection of algebraic geometry, combinatorics, and representation theory.

Email.: info@icerm.brown.edu

CIRM – Centre International de Rencontres Mathématiques

The conference will bring together leading experts and research scholars to exchange and share their experience and research results on all aspects of mathematical physics and to promote transference of knowledge at the crossroads of mathematics and physics. There will be plenary sessions (30 to 40min), short talks and posters for student presentations. The scope of the conference will be quite broad, including in particular the following topics: polyanalytic function theory, harmonic analysis, representation theory and quantization, Clifford analysis and applications, coherent states, time-frequency analysis and wavelets, orthogonal polynomials, special functions and q-analogues, Hopf algebras and quantum groups, geometric mechanics and symmetry, exact solvable systems, spectral theory and quantum systems, topological methods. With the goal of encouraging communication and collaborative research between the participants, a feature of ICMMP2021 will be the inclusion of specific time-slots for scientific discussion.

Tél.: [(212) (0) 663564850];     Email.: mouayn@gmail.com

Harmonic analysis, representation theory and quantization, Clifford algebras, Clifford analysis and applications, Coherent states & wavelets, q-deformation, Hopf algebras and quantum groups, Geometric mechanics and symmetry, Orthogonal Polynomials, special functions and exact solvable systems, Spectral theory and quantum systems, Topological Methods

Physique mathématique,    Théorie des groupes

CIRM – Centre International de Rencontres Mathématiques

ICERM

The workshop will revolve around the interplay between algebraic geometry and combinatorial structures such as graphs, polytopes, and polyhedral complexes. In particular, the workshop will foster dialogue among groups of researchers who use similar combinatorial geometric tools for different purposes within algebraic geometry and adjacent fields. The topics covered will include Newton-Okounkov bodies, Ehrhart theory, toric geometry, tropical geometry, matroids, and interactions with mirror symmetry.

Email.: Info@icerm.brown.edu

CIRM – Centre International de Rencontres Mathématiques

CIRM IHP PROGRAM

Mathematical Sciences Research Institute (MSRI)

The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.

MRSI – Mathematical Sciences Research Institute, Berkeley

The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.

Réseaux de neurones et intelligence artificielle, apprentissage automatique,    Neurologie

University of Gothenburg and Chalmers University of Technology Chalmers Tvargata

The conference aims at bringing together experts and younger mathematicians working on operator algebras and noncommutative geometry in particular from Scandinavia. The focus of the conference is on fostering new interactions between operator algebras and noncommutative geometry coming forth from recent developments in both areas.

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.

Cours et évènements pour étudiants en mathématiques,    Algèbre

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.

Cours et évènements pour étudiants en mathématiques,    Calcul infinitésimal, équations différentielles et intégrales

CIRM – Centre International de Rencontres Mathématiques

American Institute of Mathematics, San Jose

This workshop, sponsored by AIM and the NSF, will be devoted to analysis on the hypercube. The topics of the workshop will include harmonic analysis on the hypercube, Markov-Bernstein type inequalities, and martingales and Bellman functions.

Algèbre,    Mécanique quantique et l'information quantique

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

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.

Cours et évènements pour étudiants en mathématiques,    Algèbre

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

Cours et évènements pour étudiants en mathématiques,    Algèbre

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

Cours et évènements pour étudiants en mathématiques,    Analyse

Applied and computational topology, one of the most rapidly growing branches of mathematics, is becoming a key tool in applied sciences. It is making impact not only in mathematics, but on the wide interdisciplinary environment including material and medical sciences, data science, robotics.

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.

Cours et évènements pour étudiants en mathématiques,    Théorie des groupes

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.

Analyse,    Cours et évènements pour étudiants en mathématiques

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.

Algèbre,    Cours et évènements pour étudiants en mathématiques

University of Portsmouth, School of Mathematics and Physics

Tél.: [02392846358];     Email.: ittay.weiss@port.ac.uk

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.

Cours et évènements pour étudiants en mathématiques,    Théorie des nombres, arithmétique

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.

Cours et évènements pour étudiants en mathématiques,    Théorie des nombres, arithmétique

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.

Algèbre,    Cours et évènements pour étudiants en mathématiques

The Euler International Mathematical Institute, Saint Petersburg

Affine algebraic geometry studies algebraic subvarieties of complex affine space C^n. A major contributor to this field in the following generation is Shulim Kaliman, whose work this conference is intended to honor on the occasion of his 70th birthday. The conference will feature 10-12 prominent plenary speakers from among Kaliman's research colleagues, such as Mikhail Zaidenberg, with additional talks that include younger researchers. Kaliman's work draws from an impressive range of tools, not only in algebra and geometry but also in topology and analysis. The title of the conference reflects this: the embeddings, automorphisms, structure and topology of affine varieties are themes running throughout Kaliman's work. The talks will focus on current trends within these themes, and will not only bring together active researchers in the field but will also seek to engage students and early career researchers in the study of affine algebraic geometry.

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.

Cours et évènements pour étudiants en mathématiques,    Algèbre

Society for Industrial and Applied Mathematics (SIAM)

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.

Cours et évènements pour étudiants en mathématiques,    Algèbre

Brno University of Technology, Faculty of Mechanical Engineering, Brno, Czech Republic.

The conference has three main goals: To promote the development of the geometric algebra and geometric calculus. To spread geometric algebra technologies within industry and business by showing a range of applications (image processing, computer vision, robotics, flight navigation, molecular geometry, etc.). To make progress on the inclusion of geometric algebra ideas into the mathematics, physics, computer science and engineering curricula.

Algèbre,    Théorie de l'information, fondations de l'informatique

Clay Mathematics Institute (CMI)

Spectral geometry, calculus of variations, and elliptic PDEs are a central part of modern analysis and geometric analysis. At the same time, these have important applications in other sciences, in particular mathematical physics. This workshop aims to bring together leading experts in these fields to discuss the main developments and open questions. The main research themes of the workshop include shape optimisation and sharp functional inequalities, Robin boundary value problems, Steklov eigenvalue problems, and properties of eigenfunctions and solutions to elliptic PDEs.

Algèbre,    Calcul infinitésimal, équations différentielles et intégrales

Society for Industrial and Applied Mathematics (SIAM)

Physique numérique,    Simulation

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

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

CIRM – Centre International de Rencontres Mathématiques

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

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.

Théorie des groupes,    Théorie des nombres, arithmétique

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.

Cours et évènements pour étudiants en mathématiques,    Calcul infinitésimal, équations différentielles et intégrales

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

CIRM – Centre International de Rencontres Mathématiques

CONFERENCE

CIRM – Centre International de Rencontres Mathématiques

CONFERENCE

CIRM – Centre International de Rencontres Mathématiques

CONFERENCE

CIRM – Centre International de Rencontres Mathématiques

CONFERENCE

CIRM – Centre International de Rencontres Mathématiques

RESEARCH SCHOOL

Stability, Boundedness and Fano Varieties at the Beijing International Center for Mathematical Research.