Conferences  >  Mathematics  >  Algebra  >  United States

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

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.

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.

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.

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?

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.

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.

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.

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.

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.

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.

Massachusetts Institute of Technology (MIT)

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.

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

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