Conferences  >  Mathematics  >  Algebra

University center of Barika, Algeria

Number Theory, Arithmetic,    Group Theory

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.

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.

MPI f. Mathematik, Bonn

Algebraic K-theory is an object that sits at the centre of large parts of algebra, geometry, and topology because of its universal role as a receptacle to count other mathematical objects with signs. However, since its invention, a phenomenon often called the Eilenberg swindle - which says that the algebraic K-theory of a category which is too large must necessarily be zero - has been accepted as a fundamental limit to the theory. Recently, Alexander Efimov introduced a construction called continuous K-theory which allows one to make sense of algebraic K-theory of certain large categories known as dualisable categories in a nontrivial way, thus surmounting the problem of the aforementioned Eilenberg swindle. These dualisable categories encompass geometrically interesting and previously inaccessible examples such as sheaves on locally compact Hausdorff spaces. This new direction in K-theory has seen many recent advancements such as the rigidity of non-commutative motives by Efimov and the polynomial functoriality of continuous K-theory by Akhil Mathew and collaborators.

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

Universidad Complutense de Madrid

Mathematical Physics,    Geometry and Topology

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.

Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz

Email: icdgfez2024@gmail.com

Geometry and Topology,    Analysis

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

Massachusetts Institute of Technology

Email: kristims@mit.edu

Representation, group, Lie algebra

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

Institute for Pure & Applied Mathematics (IPAM)

Over the last half a century, Algebra, Combinatorics, and Discrete Geometry have undergone transformations due, in part, to the connections each of these areas have to other fields and the growth of computational approaches used in the study of theoretical mathematics. These areas are closely intertwined, with various algebraic, combinatorial, and geometric objects playing pivotal roles. These objects include monomial ideals, affine semigroup rings, Stanley-Reisner rings, Ehrhart rings, toric rings, Cox Rings, Chow Rings, Gröbner bases on the algebraic side; graphs, matroids, simplicial complexes, polytopes and polyhedral complexes, convex bodies, posets, lattices, arrangements of hyperplanes on the combinatorial and discrete geometry side.

Graph Theory and Combinatorics,    Numerical Analysis and Computational Mathematics

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)

Our meeting will bring together researchers in various fields of mathematics such as Geometry, Combinatorics and Algebra. Through scientific talks new directions will be given and open problems will be proposed aiming at new collaborations among the participants.

Geometry, Combinatorics, Commutative Algebra.

Graph Theory and Combinatorics,    Geometry and Topology