Conferences  >  Mathematics  >  Algebra

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

CIRM – Centre International de Rencontres Mathématiques

Geometry and Topology,    Number Theory, Arithmetic

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

Geometry and Topology,    Graph Theory and Combinatorics

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

In this workshop we will study infinite-type surfaces and their mapping class groups from several perspectives. Each participant will be asked to either give a lecture or run a problem session.

Geometry and Topology,    Group Theory

Isaac Newton Institute for Mathematical Sciences (INI)

The programme will start with an introductory school on equivariant methods in algebraic and differential geometry for graduate students, postdocs and those who are interested in learning background material for the programme.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

American Institute of Mathematics, Pasadena, California

This workshop, sponsored by AIM and the NSF, will be devoted to connections between automorphic forms, algebraic cycles, and intersection theory. Many phenomena in automorphic forms have interesting analogues in algebraic or arithmetic geometry. One key example is provided by Kudla and Kudla-Millson’s generating series of special cycles, which are geometric analogues of theta series. Another is the Gan-Gross-Prasad period integral, which also has an arithmetic analogue in terms of intersections of special cycles. The workshop’s goal is to further develop instances of these known analogies, and to explore new ones, involving novel tools like derived algebraic geometry.

Institute for Pure & Applied Mathematics (IPAM)

The workshop aims to bring together researchers whose work involves the exploration of symmetric categorical structures in different contexts such as Hopf algebras, tensor categories, Lie superalgebras, homological algebra, and representation theory. The meeting will promote an exchange of ideas within researchers at different stages of their careers, and we hope to leave ample time for open-ended conversation and collaborative discussion.

Institute for Computational and Experimental Research in Mathematics (ICERM)

This workshop focuses on connections between higher-order statistics and symmetric tensors, and their applications to machine learning, network science, and other domains. Higher-order statistics refers to the study of correlations between three or more covariates. This is in contrast to the usual mean and covariance, which are based on one and two covariates. Higher-order statistics are needed to characterize complex data distributions, such as mixture models. Symmetric tensors, meanwhile, are multi-dimensional arrays. They generalize covariance matrices and affinity matrices and can be used to represent higher-order correlations. Tensor decompositions extend matrix factorizations from numerical linear algebra to multilinear algebra. Recently tensor-based approaches have become more practical, due to the availability of bigger datasets and new algorithms. The workshop brings together applied mathematicians, statisticians, probabilists, machine learning experts, and computational algebraic geometers. Presentations will expose how symmetric tensors, with nonlinear algebra and non-convex optimization, provide natural mathematical machinery for exploiting higher-order interactions. Topics include moment tensor decompositions; spectral methods for hypergraphs; and related random matrix theory.

Email: info@icerm.brown.edu

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

Research Institute for Mathematical Sciences (RIMS)

Higher Dimensional Algebraic Geometry: James 60 is a conference highlighting recent progress in higher-dimensional algebraic geometry scheduled in honor of James McKernan's 60th birthday. The conference will focus on the many areas of algebraic geometry impacted by the groundbreaking work of James and his collaborators.

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

CIRM – Centre International de Rencontres Mathématiques

The aim of this CIRM-SMF week is first to provide a basic and complete introduction to o-minimality and Hodge theory, and then to give a presentation of the recent applications of o-minimality to Hodge theory, for an audience of non-experts, with a special attention to junior researchers. Our hope is that this week will provide all technical tools, both in o-minimality and Hodge theory, to young researchers, and make possible to develop some new bridges between senior researchers in Model Theory and Hodge Theory.

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

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics

Isaac Newton Institute for Mathematical Sciences (INI)

This workshop focuses on the following themes and their interactions: 1. Geometric and equivariant aspects of algebraic statistics 2. Computation of invariants in algebraic (especially toric) geometry 3. Algebraic group actions on combinatorial spaces

Geometry and Topology,    Graph Theory and Combinatorics

Research Institute for Mathematical Sciences (RIMS)

Simons Laufer Mathematical Sciences Institute (SLMath)

The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field. It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

Commutative rings, computational commutative algebra, D-modules, free resolutions, Gröbner deformations, Homological conjectures, Lech's conjecture, maximal Cohen-Macaulay modules, McKay correspondence, mixed characteristic, multiplicities, perfectoid spaces, prismatic cohomology, symbolic powers, syzygies, Tight closure theory

Mathematical Sciences Research Institute (MSRI)

The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field. It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

American Institute of Mathematics, Pasadena, California

This workshop, sponsored by AIM and the NSF, will be devoted to problems and questions about the non-vanishing of automorphic periods, especially existence and potential applications. Past progress on such problems has found applications in works on the Birch--Swinnerton-Dyer conjecture, on non-vanishing of Iwasawa invariants of p-adic L-functions, and the finiteness of rational points on certain varieties.

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

CIRM

GAGTA conferences form an annual series of conferences devoted to the dialogue between different approaches on infinite groups: Geometry, combinatorics, decidability, logic and algorithms. These conferences gather every year a group of involved specialists and focus on giving good opportunities to young researchers. They both contribute to long term research thematics and explore new trends. Growth of groups, metric properties as initiated by M. Gromov, computation, algorithms and logic in infinite groups are the main lines of theses conferences. Cubic groups, contracting elements in almost hyperbolic groups, random walks on groups, dynamical systems, various aspects of normal forms in specific groups, automata groups and self-similar groups are some of the current hot topics. All in all, these conferences are a meeting point between algebra, geometry and computer science. In this venue of GAGTA, we will also emphasize the strong links with symbolic dynamics as well as the strengths of Sage software for computing in group theory.

Geometry and Topology,    Group Theory

Institute for Pure and Applied Mathematics (IPAM), UCLA

Many-body quantum mechanical systems are described by tensors. If a system has n particles, its state is an element of H1⊗⋯⊗Hn, where Hj is a Hilbert space associated to the j-th particle. Due to the exponential growth of the dimension of H1⊗⋯⊗Hn with n, any naive method of representing these tensors is intractable on a computer. However, most tensors are unlikely to appear as quantum states. Tensor network states were defined to reduce the complexity of the spaces involved by restricting to a subset of tensors that is physically reasonable. States of physical interest seem to be well parameterized as tensor networks with a small number of parameters. The construction essentially consists of a decorated graph, and the structure of the graph determines which tensors can be constructed from the configuration. This leads to questions regarding the best (still tractable) structures for graphs. Approximating a state in terms of a tensor network makes the entanglement nature of the state itself apparent, which is not visible when approximating the state in a physical coordinate system. Recently a tensor network on a classical computer apparently was more effective than Google’s quantum computer. In this workshop we will compare the computational advantages of quantum computing vs tensor networks. It is important to investigate this question both practically and theoretically. Beyond tensor networks, the workshop will explore additional classes of tensors useful for many-body physics and quantum information theory and their utility in areas such as high dimensional probability.

Research Institute for Mathematical Sciences (RIMS)

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

Analysis,    Geometry and Topology

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

Courses and Events for Math Students and Early Career Researchers,    Analysis

Goethe University Frankfurt am Main

This conference is funded by the CRC 326 Geometry and Arithmetic of Uniformized Structures (GAUS).

CIRM – Centre International de Rencontres Mathématiques

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

This is the fourth instalment of the THGT conference series. As its predecessors, the conference takes place in Bielefeld in spring, and as before it welcomes researchers studying groups through their interactions with topology and homology, as well as people interested in entering the subject.

Geometry and Topology,    Group Theory

Isaac Newton Institute for Mathematical Sciences (INI)

The workshop focuses on recent equivariant techniques in enumerative geometry of holomorphic maps between complex manifolds. It will bring together researchers working on global singularity theory (multisingularity classes of holomorphic maps, Thom polynomials, multiple-point formulas), and on complex manifolds with positivity properties (hyperbolicity, ample cotangent bundle, jet differentials). The mini-courses aim to explain the central role of the Hilbert scheme of points on complex manifolds in these problems.

American Institute of Mathematics (AIM)

The study of degree d points on algebraic curves over ℚ is a rich and mature area of research, with the Abel-Jacobi map and the Mordell-Lang conjecture providing powerful tools for exploration. However, for higher dimensional varieties there is no such approach that works in general. Because of this, we lack even a conjectural framework for understanding which higher dimensional varieties over ℚ should have "many" degree d points. The workshop will focus on questions aimed at addressing this dearth, concentrating on the case of algebraic surfaces. For instance, what does it mean for a surface over ℚ to have "many" degree d points? What are some geometric constructions that give rise to abundant degree d points? Are these related to geometric measures of irrationality? If HilbdX has a Zariski dense set of ℚ-points for some small d, does that yield any arithmetic or geometric consequences for X? If X embeds into its Albanese, can we obtain results analogous to that of curves?

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

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

Courses and Events for Math Students and Early Career Researchers,    Geometry and Topology

Simons Laufer Mathematical Sciences Institute (SLMath)

This workshop will give an overview of recent developments in non-commutative algebraic geometry, including NC projective AG, NC resolutions, semiorthogonal decompositions, enhancements of derived categories, and connections to homological mirror symmetry, to enumerative AG, to moduli spaces and to birational geometry. It will in particular focus on speakers who have built new bridges between these topics.

Mathematical Sciences Research Institute (MSRI)

This workshop will give an overview of recent developments in non-commutative algebraic geometry, including NC projective AG, NC resolutions, semiorthogonal decompositions, enhancements of derived categories, and connections to homological mirror symmetry, to enumerative AG, to moduli spaces and to birational geometry. It will in particular focus on speakers who have built new bridges between these topics.

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

ICMS - International Centre for Mathematical Sciences

As first observed by Mazur and Mumford, there exists a deep analogy between 3-manifolds and number fields. In the 90s, Morishita expanded upon and delved deeper into these connections between low-dimensional topology and number fields. More recently, Minhyong Kim proposed that, in line with the aforementioned analogy, one should develop “arithmetic field theories” for number fields. Kim’s proposal invigorated interest in this area of study, leading to a plethora of new research directions. Examples include the work of Kim and collaborators, as well as connections to the Langlands program explored by Ben-Zvi—Sakellaridis—Venkatesh. The once-unexpected comparison between 3-manifolds and number fields is now proving fruitful, and it promises to illuminate number theory, potentially leading to significant breakthroughs. This workshop will bring together experts and young researchers to further explore a field that is still largely unexplored. While the analogies are striking, we believe that the field has not yet seen its full potential. One of the goals of the workshop is to find new problems which can be attacked with ideas stemming from the analogy between number fields and 3-manifolds.

Institute for Pure and Applied Mathematics (IPAM)

We have seen how probability motivates new research directions in algebraic combinatorics and how algebraic combinatorics leads to new discoveries in probability. The aim of the workshop is to further stimulate the cross-infiltration of the ideas between two fields.

Part of the Long Program Geometry, Statistical Mechanics, and Integrability

Simons Laufer Mathematical Sciences Institute (SLMath)

Many long-standing conjectures in commutative algebra have been solved in recent years, often through the introduction of new methods that are quickly becoming central to the field. This workshop will bring together a wide array of researchers in commutative algebra and related fields, with the goal of forging new connections among topics, and with a particular emphasis on transformative new methods.

Commutative rings, modules, ideals, mixed characteristic, Frobenius powers, test ideals, tight closure, perfectoid methods, singularities, birational algebraic geometry, multiplier ideals, symbolic powers, syzygies, free resolutions, homological methods, derived categories, polynomials, monomial ideals, toric varieties, Schubert varieties, combinatorial commutative algebra, equivariant ideals, maximal Cohen-Macaulay modules, applications of representation theory, twisted commutative algebras, D-modules, local cohomology, computational commutative algebra, graded rings and projective varieties

Mathematical Sciences Research Institute (MSRI)

Many long-standing conjectures in commutative algebra have been solved in recent years, often through the introduction of new methods that are quickly becoming central to the field. This workshop will bring together a wide array of researchers in commutative algebra and related fields, with the goal of forging new connections among topics, and with a particular emphasis on transformative new methods.

CIRM – Centre International de Rencontres Mathématiques

Group Theory,    Geometry and Topology

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

Simons Laufer Mathematical Sciences Institute (SLMath)

This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

Lie algebras, Representation theory, combinatorics

Mathematical Sciences Research Institute (MSRI)

This workshop will have a view to the future of a broad spectrum of topics including structure and classification of finite dimensional Lie algebras and superalgebras in characteristic p structure of infinite dimensional Lie algebras and their representations deformation theory of algebras, double constructions and elemental Lie algebras diagram algebras and combinatorial representation theory algebraic combinatorics of groups of Lie type:characters, Schur-Weyl duality, Bratteli diagrams, and McKay correspondences quantum groups and crystal bases, particularly for superalgebras and affine algebras examples of fusion categories arising from representations of Drinfeld doubles and other algebras cohomology for finite tensor categories with applications to its underlying geometry

This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

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

CIRM – Centre International de Rencontres Mathématiques

The aim of the present conference is to gather mathematicians working in Algebra, Geometry, Topology, and Mathematical Physics. Created over the past 50 years, the theory of higher structures (operads, homotopy algebras, infinity-categories) has given rise recently to powerful tools which led to resolutions of open problems and prompted deep developments, for instance in algebraic topology (faithful algebraic invariants of the homotopy type of spaces), algebraic geometry (derived algebraic geometry), and deformation theory (formal moduli problems). More recent, fundamental achievements have been obtained by applying these effective and algorithmic higher algebraic methods in Lie theory (higher Lie theory), derived deformation theory (deformation theory in positive characteristic, universal deformation groups, Grothendieck–Teichmüller groups), homotopy theories (rational homotopy theories), and geometry (algebraic, complex and discrete).

This conference is devoted to the areas of L-functions and autmorphic forms. In particular, it focusses on the interactions between both fields, which have a long and fruitful history since the fundamental work by Hecke about 90 years ago. The topics will focus on new developments around the areas indicated in the title, as well as establishing and furthering dialogue on new developments at the boundary of these areas. Given the ubiquity of automorphic forms throughout number theory as well as their strong interaction with the field of L-functions, it is very reasonable to expect that both areas will benefit from each other in the future as well. It is likely that this would lead to ideas more broadly useful in other areas of pure mathematics as well as to new types of objects to inspect and new structural questions within both fields.

Society for Industrial and Applied Mathematics (SIAM)

Isaac Newton Institute for Mathematical Sciences (INI)

The goal of this conference is to bring together researchers in complex algebraic and differential geometry, working on notions of stability for algebraic varieties such as K-stability (and in particular the construction of moduli spaces of algebraic varieties), the existence of canonical metrics in Kähler geometry and the many nearby topics that interact with these areas. The relationship between K-stability and the existence of canonical Kähler metrics goes by the name of the Yau-Tian-Donaldson conjecture, and is motivated by a more classical correspondence between stability in the sense of geometric invariant theory and properties of moment maps as used in symplectic geometry—two of the overarching themes of the wider programme. This conference will emphasise the deep links between Kähler geometry, stability conditions and various related problems in equivariant algebraic and differential geometry.

Centre de recherches mathématiques (CRM)

Institute for Pure and Applied Mathematics (IPAM)

The interplay of integrable models of statistical mechanics with combinations of probability theory and algebraic methods such as transfer matrix formalism, diagram algebras, and quantum group techniques, has proved fruitful in the past decades in both mathematics and physics. It has been particularly beneficial to enhance interactions between researchers working at the interfaces of these areas. The aim of this workshop is to bring together experts in algebraic and probabilistic aspects of solvable lattice models as well as researchers working on related algebraic subjects who have a common interest in understanding universal phenomena such as KPZ behavior, limit shapes, and convergence of lattice models to CFT predictions. In particular, we aim to develop interactions between different approaches to the study of lattice models, such as Bethe ansatz, (inhomogeneous) CFT methods and the tangent method. Other topics of potential interest include multi-species, forest fires and sandpile models, for which such interactions are less developed as for now. We also intend to foster interactions between researchers studying quantum groups and CFT on the one hand and probabilists working on SLE/CLE topics on the other, hoping for a fruitful synthesis of ideas and techniques.

Oklahoma State University in Stillwater

Over the last 36 years, the Annual Workshop on Automorphic Forms and Related Topics has remained a small and friendly conference. This year the conferece will take place May 20-24th in Stillwater, Oklahoma. Those attending range from students to new PhD's to established researchers. For young researchers, the conference has provided support and encouragement. For accomplished researchers, it has provided the opportunity to mentor as well as a forum for exchanging ideas. The workshop has become internationally recognized for both its high-quality research talks and its supportive atmosphere for junior researchers. Participants present cutting-edge research in all areas related to automorphic forms. These include mock modular forms, Maass wave forms, elliptic curves, Siegel and Jacobi modular forms, special values of L-functions, random matrices, quadratic forms, applications of modular forms, and many other topics.

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

University of Georgia, Athens, GA, USA

The aim of this conference is to bring together a diverse array of leading mathematicians in algebra and representation theory to promote future collaborations and inspire a new generation of mathematicians to work on exciting problems in these fields.

Cohomology and Modular Representation Theory, Representations of Lie (Super)algebras, Geometric Representation Theory, Noncommutative Algebraic Geometry.

The American University of Beirut / Centre International de Mathématiques Pures et Appliquées (CIMPA)

The relation between modular forms and their corresponding L-functions with various disciplines of mathematics has undergone significant evolution in the past century due to the critical role these complex analytical functions play in resolving essential problems and conjectures. The connection of modular forms and their L-functions with number theory, elliptic curves, representation theory, and algebraic geometry, among others, have resulted in diverse generalizations in different directions. The primary objective of the summer school is to acquaint graduate students in Lebanon and other regions with different types of modular forms and their practical applications. The school is designed to be spread over two weeks, with the first week serving as an introduction to basic concepts and the second week focusing on advanced and contemporary developments. In addition to the mini-courses, the program includes a programming tutorial intended to provide students with opportunities to interact directly with the computational aspect of the theory.

CIRM – Centre International de Rencontres Mathématiques

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

Centre de recherches mathématiques (CRM)

The “Comparative Prime Number Theory” symposium is one of the highlight events organized by the PIMS-funded Collaborative Research Group (CRG) “L-functions in Analytic Number Theory”. It is a one-week event taking place on the UBC campus in Vancouver, B.C., Canada from June 17–21, 2024. Comparative prime number theory certainly includes prime number races, both classical (Chebyshev's bias) and over number fields and function fields. It also broadly includes the distribution of zeros of L-functions associated with these prime counting functions, including topics related to the Linear Independence hypothesis (LI) on the imaginary parts of those zeros, as well as general oscillations of number-theoretic error terms.

Isaac Newton Institute for Mathematical Sciences (INI)

The workshop focuses on the role of equivariant techniques in enumerative geometry and moduli stacks. It will bring together researchers working on the relationship between concepts of stability and wall-crossing in different settings such as moduli stacks, geometric invariant theory, Bridgeland stability and K-stability, as well as enumerative geometers studying the geometry and topology of Hilbert schemes of points on surfaces and higher dimensional manifolds and related invariants.

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

Algebraic geometry is the field of mathematics which concerns the study of spaces cut out by polynomial equations. This workshop concern the interaction of two important objects in algebraic geometry - the K-groups and the Brauer group. In algebraic geometry, we study spaces via invariants - the procedure of attaching simpler, more "linear" objects to these spaces in the hope of extracting information about them. Both the K-groups and Brauer group are such examples which have had an excellent track record in being both powerful and accessible at the same time. Roughly speaking, the K-groups are built out from \emph{vector bundles} on such a space - a continuous assignment of vector spaces on each point of the space. On the other hand the Brauer groups are built from "twisted" vector bundles. Both invariants have had a history of interaction and cross-pollination and the goal of the workshop is to bring together researchers in both areas to share their research and pave the way for even more fruitful interaction in the future. We are particularly excited about the prospect of new, field-driving questions to come out from this workshop.

Courses and Events for Math Students and Early Career Researchers,    Group Theory

University of Milan, Department of Mathematics, Italy and CIC Cuernavaca, Mexico

The conference welcomes experts and students in the subject of nonlinear mathematical physics, where the focus is on the development and use of mathematical theories to analyse and solve nonlinear problems that arise in nature and in technologies. Participants can present their recults orally or in the form of a poster. The main subjects include nonlinear continuous and discrete integrable equations, non-commutative geometry, symmetry analysis, wave propagations, and the classification of equations. One evening of talks is reserved for the non-expert audience where the general public is invited to listen to presentations which will be of a non-technical and more philosophical nature. This open-door session is titled "An Evening of Science and Philosophy" and participation is free for everyone.

Email: Dr.Norbert.Euler@gmail.com

Nonlinear Continuous and Discrete Equations, Integrable Equations and Applications, Non-Commutative Geometry, Symmetry Analysis, Nonlinear Flows, Wave Propagation Mathematics in Fluid Mechanics and Geophysics, Classification of Nonlinear Equations, Lie and Lie Superalgebras, Representation Theory, Dynamical Systems, Chaos

Mathematical Physics,    Group Theory

SFB 1085 Higher Invariants at the Faculty of Mathematics at the Universität Regensburg

Analysis,    Courses and Events for Math Students and Early Career Researchers

The International Centre for Mathematical Sciences (ICMS)

Hilbert’s twelfth problem asks for explicit constructions of the abelian extensions of a given number field, similar to what is known for the rational numbers and for imaginary quadratic fields. The workshop will focus on the breakthroughs in [DKa] and [DKb], with a lecture series by the two authors forming the cornerstone of the activity.

Centre de recherches mathématiques (CRM)

Banach Center

ICMS, Bayes Centre, Edinburgh

The idea of p-adic families of automorphic forms grew out of work of Serre and Swinnerton-Dyer in the 70s exploring congruences between the q-expansion coefficients of modular forms. Work of Hida, Coleman and Mazur made the investigation of p-adic families one of the central topics in the arithmetic of modular forms. In the following decades there were striking applications to the construction of p-adic L-functions, Iwasawa theory and modularity of Galois representations. One powerful organising principle has been to parametrize p-adic modular forms (or, more generally, p-adic automorphic forms) by p-adic analytic spaces known as eigenvarieties (or eigencurves, in the one-dimensional case originally considered by Coleman and Mazur). Our understanding of the geometry of eigenvarieties and their relationship to moduli spaces of Galois representations has rapidly developed, but there are still many important open questions. An overarching objective of this meeting will be to bring together people working on the different theories of p-adic automorphic forms and various applications (or potential applications). We hope that this will inspire new collaborations and insights.

Massachusetts Institute of Technology (MIT)

CIRM – Centre International de Rencontres Mathématiques

The core problem of this project stems from the heuristic articulated by many authors in mathematics and mathematical physics over an extended period, that when q 2 is a primitive ` th root of unity, there is a connection between limn→∞ TLn(q) where TLn(q) is the Temperley-Lieb algebra on the one hand, and the Virasoro algebra L = ⊕i∈ZCLi ⊕ CC on the other. The search for such a connection has hitherto led to many tantalising analogies, but as yet no definitive theorems. We shall pursue two distinct approaches to the problem.

Simons Laufer Mathematical Sciences Institute (SLMath)

In the last few years, there have been extraordinary developments in many aspects of curve theory. Beginning with many examples in low genus, this summer school will introduce the participants to the background behind these developments in the following areas: moduli spaces of stable curves Brill–Noether theory the extrinsic geometry of the curves in projective space We will also include an introduction to some open problems at the forefront of these active areas.

Banach Center

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

Probability and Statistics, Game Theory,    Geometry and Topology

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

Simons Laufer Mathematical Sciences Institute (SLMath)

This workshop will include introductory lectures on each of the four main topics of the program: geometric flows, geometric problems in mathematical relativity, global Riemannian geometry, and minimal submanifolds. The workshop will also have semi-expository lectures on recent advances and breakthroughs involving interactions between the four main topics. This will set the stage and provide important context for the semester-long program itself.

mean curvature flow, Ricci flow, fully nonlinear flows, general relativity, mass, Ricci curvature, scalar curvature, sectional curvature, symmetry, Riemannian geometry, group actions, minimal surfaces, stability and index

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Institute for Advanced Study in Mathematics (IASM)

The theories of rational/trigonometric/elliptic functions were developed as functions over plane/cylinder/torus, respectively, before the 20th century. Among them, the theory of elliptic functions is most interesting, and it can be understood as the parent theory of the rest. During the 20th century, the same rational/trigonometric/elliptic trichotomy has been also found in integrable systems, algebras and cohomology groups. Like the theory of functions, recent development reveals that the relationship among integrable system, algebra, geometry, and physics becomes most profound at elliptic level. In particular, Lie algebras (rational) are promoted to affine Lie algebras (trigonometric) and toroidal Lie algebras (elliptic). The workshop aims at investigating quantum versions of toroidal Lie algebras, called quantum toroidal algebras.

Mathematical Physics,    Geometry and Topology

CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

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

The UK Spectral Theory Network aims to strengthen the research interaction among people working in spectral theory and adjoining fields in the UK. It offers Early Career Researchers, PhD students and members of the network an effective platform for exploring connections between the multifaceted strands of the subject, exchanging ideas and developing new collaborations. It promotes equality, diversity and inclusion in mathematics, and inspires future generations of researchers in the field.

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

CIRM – Centre International de Rencontres Mathématiques

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

Courses and Events for Math Students and Early Career Researchers,    Group Theory

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

Graph Theory and Combinatorics,    Group Theory

SFB 1085 Higher Invariants at the Faculty of Mathematics at the Universität Regensburg

Analysis,    Courses and Events for Math Students and Early Career Researchers

Institute for Advanced Study in Mathematics (IASM)

This workshop will tackle some fundamental open questions about Artin-Schelter regular algebras, in particular, elliptic algebras, and their associated Poisson structures. In particular, it will focus on the correspondence between the representations of elliptic algebras and the symplectic leaves of their semi-classical limits, as well as on the relationship between the deformation theory of Artin-Schelter regular algebras and that of the derived category or the A-infinity-category of related projective schemes. This workshop brings together leading experts in algebra and geometry from around the world to identify and attack these outstanding problems and to collaborate for future breakthroughs.

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

Courses and Events for Math Students and Early Career Researchers,    Group Theory

CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

Isaac Newton Institute for Mathematical Sciences

Over the past few years, several remarkable links between quantum information, quantum groups, and operator algebras have been discovered. This includes in particular the study of non-local games, quantum automorphism groups, and the resolution of Connes’ Embedding problem announced by Ji, Natarajan, Vidick, Wright and Yuen in 2020. The focus of this workshop is the state of the art in this highly active area, covering the latest developments and potential future directions.

Isaac Newton Institute for Mathematical Sciences

Equivariant techniques have played a critical role in the proofs of several major results and developments in algebraic topology over the past decade. Examples include the solution of the famous Kervaire invariant one problem, computations of previously inaccessible homotopy groups of spheres based on the motivic Adams spectral sequence, and the new equivariant approach to THH, TC, and algebraic K- theory. The programme will unite experts and young researchers who apply homotopic methods in algebra (operads), algebraic topology, and algebraic geometry (motivic homotopy theory) around the common theme of equivariant methods. Though these methods have already led to significant breakthroughs, their potential is clearly far from exhausted. We foresee that this programme will incite further developments and greater synergies between equivariant homotopy theory and the themes of the programme centred around three workshops: "Operads and calculus", "Chromatic and motivic homotopy theory" and "THH, TC and algebraic K- theory".

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Simons Laufer Mathematical Sciences Institute (SLMath)

Many exciting breakthroughs in combinatorics involve innovative applications of techniques from a wide range of areas such as harmonic analysis, polynomial and linear algebraic methods, spectral graph theory, and representation theory. This workshop will present recent developments in this area and facilitate discussions of research problems.

extremal combinatorics, extremal graph theory, probabilistic combinatorics, discrete geometry, additive combinatorics, combinatorial geometry, incidence geometry, arithmetic progressions, Discrete analysis

Graph Theory and Combinatorics,    Analysis

Isaac Newton Institute for Mathematical Sciences

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Isaac Newton Institute for Mathematical Sciences

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Isaac Newton Institute for Mathematical Sciences

Equivariant homotopy theory in context

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

The Fields Institute for Research in Mathematical Sciences

Homotopy theory is in the midst of a renaissance as its usefulness in other areas of mathematics is becoming increasingly recognised. From polyhedral products in geometric group theory, to combinatorial methods in group theory, to topological properties of manifolds and spaces of embeddings, to Morava K-theory in symplectic geometry, to simplicial methods in topological data analysis, to a host of applications in mathematical physics - and these name only a few areas of interaction - homotopy theory over the past ten to fifteen years has significantly extended its reach. This program will assemble a wide range of leading experts to discuss the state of the art in current research, both in terms of core fundamental problems and crossover to other areas, and explore exciting new directions.