Conferences  >  Mathematics  >  Algebra

University center of Barika, Algeria

Number Theory, Arithmetic,    Group Theory

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.

This conference is part of a recurring series which bring together the worlds leading experts on the theory of regulators and their connections to the study of algebraic cycles and motives as well as their applications to physics and other branches of mathematics. In particular, the conference will report on the progress in the subject since the previous conference Regulators IV, which was held in Paris in 2016.

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.

This event will have three parts. From June 5th to June 7th it will feature three introductory mini-courses on the topics of configuration spaces, algebraic K-theory, and string topology accessible to graduate students and researchers in related fields outside algebraic topology. On June 8th, there will be a special event directed towards the general public and it will include two talks and a discussion session. The main research conference will take place from June 10th to June 14th and will feature talks by invited speakers as well as contributed talks. Everything will take place in (possibly different venues) in San Juan, Puerto Rico (TBD).

CIRM – Centre International de Rencontres Mathématiques

Department of Mathematics, National Institute of Technology, Calicut, India

Lie algebras and superalgebras are among the most important algebraic structures with ample applications in modern mathematics like geometry, harmonic analysis, algebra and representation theory, and number theory. Number Theory is one of the oldest and classical branch of mathematics. This conference aims to bring together researchers working in various areas of algebra and number theory to exchange knowledge and further possible collaborations.

Structure and representation theory of finite and infinite dimensional Lie algebras/Lie superalgebras, Number Theory (Algebraic Number Theory/ Modular Forms/ Automorphic Forms/ Diophantine Equations/ Partition Theory), Applications of Lie Theory to Number Theory

It has been discovered recently that the Massey product in Galois cohomology can be effectively applied to study cohomological invariants and torsors of algebraic and finite groups. This workshop will essentially focus on this new emerging approach. It will feature talks on the latest developments in Galois cohomology, cohomological invariants, torsors and applications of Massey products given by senior specialists and young researchers. A mini-course on Massey products aimed at graduate students attending the workshop is also being planned.

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.

University of Milano-Bicocca, Department of Mathematics

The third edition of the GABY conference will take place at the University of Milano-Bicocca (Milan, Italy)from June 17 through June 21, 2024. The conference is aimed mainly at young researchers working in group theory, algebras and related topics. The conference will offer the following three mini-courses: "The interplay of R-matrices and Quantum Groups" by Andrea Appel, University of Parma; "Computational group theory: bedrock and new frontiers" by Melissa Lee, Monash University; "Burnside groups and groups acting on rooted trees" by Anitha Thillaisundaram, Lund University. Participants can contribute with a talk or a poster. Some funds may be available to cover accommodation for some participants. The deadline for registering is May 31, 2024. There is a conference fee of 75€ that must be paid by May 31. The fee is reduced to 50€ for those who register and pay by April 30. The fee can also be paid upon arrival, in which case it is increased to 100€. The registration is considered complete after the payment of the fee.

Email: gaby@unimib.it

algebra, group theory, groups, quantum groups, trees, combinatorics, representation theory, graph theory, geometry,

Group Theory,    Number Theory, Arithmetic

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, investigates Shape Optimization problems for which symmetry-breaking is believed to occur: the energy functional is radially symmetric and yet its minimizer fails to enjoy full symmetry. Unlike in many other problems, the optimal shape is not the ball. The ball does solve many natural shape optimization problems for geometric and physical models, including the classical isoperimetric inequality and inequalities for capacity and the first eigenvalue of the Laplacian under Dirichlet, Robin or Neumann boundary conditions. Thus it becomes particularly fascinating to investigate problems where the ball is NOT the best, and to determine the optimal shape in those situations.

The main topics for the workshop are: Topic 1: Examples where the ball is non-optimal. Topic 2: Techniques for identifying optimal shapes: shaking, tensorization, geometric flows, first or second order arguments to prove the optimal shape must be a polygon or polytope, free boundaries analysis. Topic 3: Notable conjectures including Polya's capacity problem, Neumann spectral problems, problems from convex geometry, isodiametric capacity maximizers, Alexandrov's conjecture for intrinsic diameter.

Azerbaijan University of Architecture and Construction

The International Conference on Modern Problems of Mathematics, Mechanics and their Applications, June 19-21, Baku, Azerbaijan, will be held under the organization of the Ministry of Science and Education of the Republic of Azerbaijan, Azerbaijan University of Architecture and Construction and Istanbul Technical University. MPMMA 2024 will provide a forum where the researches from universities and academic environments can meet to share ideas and discuss recent achievements on announced topics. Time of a plenary talk will be 45 minutes.

Orginizing Committe;     Phone: [+994553683811];     Email: aidatagiyeva1984@gmail.com

Spectral theory of differential operators Operator theory Function spaces Differential equations and applications Approximation theory Optimization theory Algebra and geometry Probability, statistics and financial mathematics CFD modelling Applied mathematics Mechanics and applications Artificial Intelligence modelling Computational Methods Data modelling Computational Geometry Computational Biology

Applied Mathematics (in general),    Geometry and Topology

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

This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry.

Number Theory, Arithmetic,    Graph Theory and Combinatorics

American Institute of Mathematics (AIM)

This online workshop, sponsored by AIM and the NSF, will be devoted to formalising basic and advanced concepts in algebraic geometry. Algebraic geometry should be interpreted broadly, and could include topics in related areas such as complex differential geometry and arithmetic geometry. Formalising here means translating mathematical ideas into the language of a computer theorem prover; the prover we will use will be Lean. Works such as EGA and the Stacks project are comprehensive human-written sources for modern algebraic geometry, however they are huge and need to be triaged before a comprehensive formalisation can take place.

The main topics for the workshop are: Isolation of key formalisable goals in the area; Developing strategies to formalise key definitions and theorems (for example the Riemann-Roch theorem and its generalisations, definitions and basic facts about coherent and etale cohomology, faithfully flat descent, etale fundemantal group ...); Formalising these definitions and theorems, and PRing the work to Lean's mathematics libary; Development of a blueprint for future progress in the area.

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 International de Mathématiques Pures et Appliquées (CIMPA)

The school aims at introducing the students to a few lines of research in number theory revolving around the concepts of lattices, heights and diophantine approximation. Part of the school is devoted to presenting the recent proof by Maryna Viazovska that the densest sphere packing in dimension 8 is the one given by the E_8 lattice. In 2022 she was awarded the Fields medal. To this end we introduce the students to lattices, sphere packings and modular forms. We will prove the Cohn-Elkies bound and finally we will study Viazovska's construction of the function which optimizes such bound and proves that the E_8 lattice is the densest packing in dimension 8. In the other part of the program we will introduce the machinery of heights, which are standard tools of Diophantine geometry used to measure arithmetic complexity of objects. We will then demonstrate the use of height functions in Diophantine approximation and Diophantine geometry discussing results and conjectures such as the Mordell-Weil theorem, Faltings' theorem, Siegel's lemma, Cassels' theorem, Lehmer's conjecture, and many others. On the Diophantine approximation side, we will discuss the central themes of equidistribution and approximation of reals by algebraic numbers. We expect the participants to gain familiarity with these central and vibrant areas of mathematics that have been at the forefront of mathematical research for over a hundred years. Our program is specifically designed in a way that assumes a rather modest background, but with a concentrated and focused approach takes the audience to some of the modern-day research directions.

Centre de recherches mathématiques (CRM)

The Conference on Theoretical and Computational Algebra 2024 will be held at the University of Aveiro, in Aveiro, Portugal, from Sunday 30, June, to Friday 5, July 2024.

(Sunday 30 June is the arrival day, with only a welcome session and check-in to the venue late in the day; talks will be from Monday 1 to Thursday 4, July; departure day is Friday 5 July.)

Celebrating the Contributions of John Meakin

We are delighted to announce that the upcoming 2024 Conference on Theoretical and Computational Algebra will feature a special tribute to John Meakin. His exceptional research career and indelible mark on algebra are underscored by his thoughtful care for students and kindness.

Please come to Aveiro for a joyful gathering of distinguished scientists and friends.

Organized jointly in Timisoara by the Institute of Mathematics Simion Stoilow of the Romanian Academy and the West University in Timisoara

As usually, the conference is devoted to operator theory, operator algebras, and their applications (differential operators, complex functions, mathematical physics, matrix analysis, system theory, etc.).

Analysis,    Mathematical Physics

Geometry and Topology,    Mathematical Logic and Foundations

Banach Center

Institute for Advanced Study, Princeton, New Jersey

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)

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to connections between scissors congruence K-theory and Steinberg modules. Scissors congruence is the study of when objects such as polyhedra, manifolds, varieties, etc. are equivalent under decomposition into pieces. In the last decade, the introduction of K-theoretic constructions in the study of scissors congruence problems by Campbell and Zakharevich has seen exciting applications and opened new avenues of attack on this problem. Generalizing results for classical scissors congruence groups, Malkiewich showed that scissors congruence groups can be described as group homology with coefficients in Steinberg modules. Steinberg modules are certain representations that are relevant to the study of representations of linear groups, algebraic K-theory, and the cohomology of arithmetic groups. The goal of the workshop is to bring together researchers studying scissors congruence K-theory and as well as Steinberg modules, in order to explore interactions between the two fields.

The main topics for the workshop are: Scissors congruence K-theory Resolutions of Steinberg modules (Co)algebraic structures of Steinberg modules and scissors congruence spectra Connections with more classical forms of K-theory

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

Hebrew University of Jerusalem

The goal of this conference is explore the isogeny based cryptography for Abelian varieties of dimension $\geq 1$. The aim of this conference is to bring together mathematicians who are experts in the area of Abelian varieties and cryptographers who are focused on isogeny based cryptography. The conference is funded by a grant by NATO-Science for Peace and Security (SPS) Advanced Research Workshops (ARW)

Email: shaska@oakland.edu

isogeny, supersingular, genus two, elliptic curve, Abelian variety

Cryptography, Blockchain and Information Security,    Quantum Information Theory and Quantum Computing

Universidad de los Andes

Tropical geometry is a piece-wise linear geometry which merges ideas from algebraic, symplectic and non-archimedean geometry with tools from combinatorics and convex geometry. Via the process of tropicalization, classical varieties and geometric problems can be connected to the tropical world and, in some cases, solved there. In non-archimedean geometry, the valuation on the underlying field makes the idea of tropicalization particularly natural and powerful. In recent years, this connection has received much attention and exhibited links to diverse topics such as Hodge theory, mirror symmetry and the study of zeta functions. The main goal of this event is to introduce students and young mathematicians to these exciting topics and to foster and strengthen the connections between local researchers and the international mathematical community.

Email: p.cubideskovacsics{at}uniandes.edu.co

Tropical geometry, non-archimdean geometry

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

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)

University of Amsterdam

AGACSE 2024 is the 9th in this series of conferences and will bring together researchers from different disciplines within the Mathematics, Physics, Engineering and Computer Science communities. The conference will explore algebraic techniques for geometrical problems, study the relationships between them, and establish new links.

This conference is aimed at presenting new and interesting results in the area of automorphic forms and related topics, and is a continuation of the following series of conferences: Online Conference in Automorphic Forms (2020) and Automorphic Forms in Budapest 2022

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

University of Warwick, Mathematics Institute

Roger William Carter was a towering figure in Mathematics for over 40 years. He would be 90 in August of 2024. This memorial conference will celebrate Roger's life and scientific endeavours by bringing together a diverse group of mathematicians who knew him personally or were affected by his scientific craft.

Email: MRC@warwick.ac.uk

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

Goethe University Frankfurt

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Graph Theory and Combinatorics,    Probability and Statistics, Game Theory

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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

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

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

Isaac Newton Institute for Mathematical Sciences

Equivariant homotopy theory in context

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

Centre International de Rencontres Mathématiques (CIRM)

Centre International de Mathématiques Pures et Appliquées (CIMPA)

An L-function is a function defined additively by a Dirichlet series with a multiplicative Euler product. The initial work of Dirichlet was generalized to number fields by Hecke and given an adelic interpretation by Tate which paved the way to move from GL(1) to higher degree L functions associated to automorphic forms of GL(n) for a general n . Automorphic L functions are essentially analytic objects and allow translations between arithmetic and analysis. We recall the legendary correspondence in the case of the Riemann-ζ function, the prototype of higher L -functions both analytic and arithmetic-algebraic, between an arithmetic statement on the distribution of primes and an analytic one on the distribution of its zeros. Now there are many more parameters to explore. For example, bounding twisted automorphic forms in terms of conductors help obtain the asymptotics of representations of totally positive integers by ternary quadratic forms. The aim of this school is to prepare the participants to appreciate the contemporary theory of automorphic representations, their L -functions and their surprising links with diverse fields like Fourier analysis, algebraic geometry and theoretical physics.

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.

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)

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)