Conferences  >  Mathematics  >  Algebra

American Institute of Mathematics, Pasadena, California

This workshop, sponsored by AIM and the NSF, will be devoted to new developments in integral p-adic cohomology theories, focusing in particular on their applications to the study of integral models of Shimura varieties. The past decade has seen several innovations in p-adic cohomology, with the introduction, first of perfectoid geometry, and more recently, of prismatic cohomology and its refinements. The power of these general theories has been brought to bear on the problem of understanding the arithmetic behavior of Shimura varieties, both local and global, with applications to key number-theoretic frameworks like the Langlands and Kudla programs. The workshop’s goal is to push these applications further, and to explore new ones, with the eventual goal of obtaining a systematic and naturally functorial theory of integral models of Shimura varieties.

Universität Duisburg-Essen, Fakultät für Mathematik

This workshop aims at bringing together researchers working on various aspects (geometric, derived, etc.) of p-adic and mod p representation theory of p-adic groups. We particularly wish to offer young researchers the opportunity to present their work and build connections in an informal, friendly environment: each day will feature a couple of one hour talks by more senior speakers on the most recent advances in the area, followed by a series of 30 min talks by the junior participants.

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

Cluster algebras, webs and canonical bases are three different methods that mathematicians have developed in order the understand the symmetries of certain mathematical structures. Each of these three ways arose from, and has applications to, different areas of mathematics. These areas include algebraic geometry, representation theory, topology, and combinatorics, as well as physics. The goal of this workshop is to bring together experts and up-and-coming researchers from each of these areas in order to better understand the still mysterious connections between cluster algebras, webs, and canonical bases. A better understanding of these connections could allow for ideas from one area to be applied to solve problems in other areas.

Isaac Newton Institute for Mathematical Sciences, Cambridge

The study of the geometric properties of eigenvalues is closely linked to geometric analysis, applied mathematics and mathematical physics. A striking interplay with the theory of minimal surfaces and recently discovered connections to homogenisation theory have led to new sharp isoperimetric inequalities for Laplace and Steklov eigenvalues on Riemannian manifolds. The latest progress on Neumann and Robin eigenvalues, as well as emerging research on the spectra of other physically important operators, such as Dirac and curl, further highlight the expanding scope of the field and its applications. The workshop aims to bring together a diverse group of experts working on these and related topics. By fostering the exchange of ideas and methodologies, the meeting seeks to inspire innovative approaches to open problems and to advance the broader landscape of spectral geometry.

ICAOTA is officially supported by the African Mathematical Union (AMU), the continental organization promoting mathematical research and cooperation in Africa.

The First International Conference on Advances in Operator Theory and Applications (ICAOTA’2026) is a prestigious scientific event that will convene leading experts, early-career researchers, and professionals from across the globe to discuss recent advances in operator theory and its far-reaching applications in mathematics, physics, and engineering.

Isaac Newton Institute for Mathematical Sciences, Cambridge

From spectral shape optimization to inverse problems and computational graphics, applications of spectral problems are ubiquitous in science and engineering, and their approximation presents fascinating mathematical challenges. There are three important areas of mathematical activity which examine spectral problems from distinct perspectives: applications, computation and geometry, with important overlapping interests. In this workshop researchers will present the state-of-the-art at the intersection of these areas, and help shape an ambitious research agenda pushing the frontiers of this intersection

This conference aims to bring together postgraduate students in Algebra to showcase all the modern advances the field has to offer. We are pleased to have three invited speakers, delivering mini-courses on Geometric Group Theory, Diagrammatic algebras in Representation Theory and Quantum Algebra. We are also glad to offer postgraduate students a chance to present their own research with a call for contributed talks and posters.

Event orgnaiser;     Email: itmaia2026@gmail.com

Representation Theory, Quantum Groups, Geometric Group Theory

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

Core objects of study in algebraic geometry and in commutative algebra are called varieties and rings, respectively. Varieties are geometric objects that consist of sets of solutions to polynomial equations. Each variety has a corresponding ring consisting of the polynomial functions that are defined on the variety.

Graph Theory and Combinatorics,    Geometry and Topology

Isaac Newton Institute for Mathematical Sciences, Cambridge

The purpose of the workshop is to bring together specialists from several communities: spectral geometers, numerical analysts, and researchers working in AI geometric data processing and PDEs. The development of AI based spectral analysis requires a deep interaction between them. Our primary objective is to exchange perspectives and gain a deeper understanding of the potential role that artificial intelligence and geometric data processing may play in addressing research questions in spectral geometry, and ultimately to foster the development of new collaborations. We aim to explore how AI might provide new methods, insights, or tools that could help us tackle some of numerical problems related either to the computation of the spectrum or the optimization of the geometry in relationship with spectral functionals.

Geometry and Topology,    Neural Networks and Artificial Intelligence, Machine Learning

The International Centre for Mathematical Sciences (ICMS)

Frieze patterns are celebrated for their ubiquity in mathematics, featuring in cluster algebras, continued fraction theory, difference equations, hyperbolic geometry, and moduli space theory. This workshop brings together researchers from frieze patterns and the cognate fields of continued fractions and discrete geometry to promote cross-disciplinary interactions in these fertile subjects. The event is framed around the legacy of the English geologist John Farey (1766–1826), who inspired the development of Farey sequences and the Farey tessellation, which are common themes of the workshop. There will be a mathematical art gallery accompanying the workshop to share the outputs of our research.

CIRM

Iwasawa theory studies the p-adic variation of arithmetic objects. It was born in a series of papers of K. Iwasawa during the mid 20th century, where he studied the growth of class groups along the cyclotomic tower, and their connection to the p-adic zeta function of Kubota and Leopoldt. This result is known as Iwasawa’s Main Conjecture and it has been generalized to many other settings (elliptic curves, modular forms, etc.). This conference will bring together specialists of this domain to account for the latest advances in Iwasawa Theory. An emphasis will be put to the applications of perfectoid methods to the theory, such as in the construction of p-adic L-functions, or through the use of the Fargues–Fontaine curve and p-adic Hodge theory.

Isaac Newton Institute for Mathematical Sciences, Cambridge

There are several widely open problems about the geometry and the spectral theory of the Laplacian, many of them coming from physics, in particular from "quantum chaos'', including the statistics of the number of eigenvalues in appropriately sized intervals, which is related to the influential universality conjectures of Berry and Tabor and of Bohigas, Giannoni and Schmit; quantum unique ergodicity and Berry's random wave model; optimal lower bounds for the first eigenvalue; asymptotic estimates of Cheeger constants. Randomness plays an important role in the study of such problems. One incarnation is random wave theory, which is the study of random linear combinations of eigenfunctions. This and related models are used to understand the fine structure of nodal sets.

Simons Foundation

A conference marking the 50th anniversary of the publication of Barry Mazur's "Modular curves and the Eisenstein ideal" and Ken Ribet's "A modular construction of unramified p-extensions of Q(μ_p)". The talks will feature recent advances in areas of research that have been influenced by these two papers.

ICANTA’5 is organized by the ACSA Laboratory (Faculty of Sciences, Mohammed Premier University) in collaboration with the Ceramaths Laboratory (Université Polytechnique Hauts-de-France). This edition pays a heartfelt tribute to Professors A. Azizi, M. C. Ismaili, and M. Ziane for their inspiring research, dedication to students, and lasting service to our community. The congress brings together researchers worldwide and encourages young mathematicians to engage with current topics in algebra, number theory, and applications.

The Fields Institute

This conference will honour the work of John F. (Rick) Jardine, a professor at the University of Western Ontario. Over his 40+ year career, Rick has made foundational contributions to homotopy theory, K-theory, and topological data analysis, in particular shaping the current landscape of homotopical algebra.

CIRM

L’objectif de cette école de recherche est d’étudier certains des sujets nécessaires à la compréhension des variations p-adiques des cycles arithmétiques et de leur relation avec les formes automorphes p-adiques. Elle est principalement destinée aux doctorants et post-doctorants afin qu’ils puissent tirer le meilleur parti de la conférence qui suit.

The International Centre for Mathematical Sciences (ICMS)

This workshop centers on the representation theory of finite groups and closely related structures. Some areas of the field are well-established and classical, while others include subjects born only recently. All are being rapidly evolving and actively explored by diverse research communities. These communities, often located in different regions around the world, offer distinct perspectives and approaches to the subject. A central aim of the workshop is to bring together experts and early-career researchers from these various groups, providing a forum to share progress, exchange ideas, and ask each other questions. The workshop also offers an opportunity to celebrate Dave Benson’s 70th birthday, which falls in December 2025. Dave’s work has had a profound influence on many of the themes represented at this meeting, and we look forward to honoring his contributions during the event.

Cohomology and modular representation theory of finite groups; Hochschild cohomology; Algebraic topology; Tensor-triangular geometry; Finite tensor categories

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

Institute for Computational and Experimental Research in Mathematics

A conjecture of Malle predicts an asymptotic formula for the quantity of number fields with a given Galois group and whose discriminant is bounded by a growing parameter. This conjecture is foundational to the area of Arithmetic Statistics and has received considerable interest over the past 20 years, notably including Bhargava receiving the Fields Medal in part for his work on quartic and quintic field extensions.

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

CIRM

The International Centre for Mathematical Sciences (ICMS)

The UK has always been at the forefront of, and has a reputation in, integrable systems research. It is an area that glues together topics in mathematical physics, analysis, algebra, geometry, applied mathematics and probability. Research in non-commutative integrable hierarchies has had a recent resurgence – they have many applications, including (eg.) in non-commutative nonlinear optics, and have strong links to string theory. The main themes outlined align with, and will be led, by recent research by the invitees. We propose a different than usual workshop format, along the lines of those held at Oberwolfach and the American Institute of Mathematics. Nominated experts give feeder presentations in their areas on successive mornings, outlining the current frontier of research and open problems. In the afternoons, these are followed up by discussion sessions and working groups who report back to the workshop as a whole at the end of the day. The workshop structure develops dynamically throughout the week. The organisers and the Scientific Advisory Group meet daily to set the agenda ahead, using feedback from the end-of-day reports and participants.

(i) Regularity and solutions; (ii) Non-commutativity, both in terms of non-Abelian (eg.\/ matrix) versions of classical integrable systems and in terms of non-commutative independent variables; and (iii) The connections of such systems to random matrix theory.

Hausdorff Center for Mathematics (HCM)

In the spirit of Matthias Lesch’s life’s work, internationally renowned researchers will present recent results from the areas of singular analysis on manifolds, noncommutative geometry and functional analytic methods.

On the occasion of Matthias Lesch's 65 birthday

The International Centre for Mathematical Sciences (ICMS)

Recent research has pointed to fundamental underlying relationships between each of three sub-fields of combinatorics: matroid theory, structural graph theory, and topological graph theory. While the connection between matroids and graphs is long-established, newer foundational links with topological graph theory are creating fresh opportunities for cross-disciplinary advances. The purpose of this workshop is to provide the first dedicated forum to bring together experts in all these three fields to share techniques and approaches, and seed ongoing cross-disciplinary collaboration and advances.

Graph Theory and Combinatorics,    Geometry and Topology

Hausdorff School for Mathematics (HSM)

With this Special Topics School on "Representation Theory of Algebras and its Applications", we aim to bring together experts, young researchers, and graduate students to explore current developments in the field. The school will offer a series of introductory lecture courses on some of these recent connections, complemented by problem sessions.

Galatasaray University, Istanbul

The conference aims to bring together researchers from all areas of mathematics and science with interests in recurrence sequences, their applications and generalizations, and other special number sequences.

Fibonacci numbers, recurrence sequences, special number sequences, and applications

University of Ottawa

MMRT 2026 focuses on modern categorical and diagrammatic methods in representation theory, with particular emphasis on monoidal categories, categorification, and their applications to Lie algebras, quantum groups, and quantum symmetric pairs. The conference aims to bring together leading researchers and early-career mathematicians to exchange new techniques, highlight emerging connections with topology and quantum mathematics, and foster interaction across complementary modern approaches.

Quantum groups, quantum symmetric pairs, monoidal categories

Universitat de Barcelona

Fields Institute, Toronto, Canada

Since its inception in 1981, the IWOTA has been at the forefront of fostering collaboration and advancing research in the field of operator theory and its diverse applications. Beginning as a modest gathering, IWOTA has evolved into a prestigious conference series, attracting leading mathematicians and engineers from around the globe. IWOTA has a rich history of conferences held in various countries, reflecting its global impact and reach. The diverse array of topics covered by IWOTA conferences underscores the interdisciplinary nature of operator theory and its applications. From differential equations to mathematical physics, IWOTA provides a platform for researchers to explore cutting-edge developments and collaborate on innovative solutions to complex problems.

Hausdorff Center for Mathematics (HCM)

Tensor categories are a fundamental concept in modern representation theory, with deep connections to representations of finite and algebraic groups, commutative algebra, algebraic geometry, low-dimensional topology, mathematical physics, categorification, and higher categories. In recent years, several astonishing discoveries have been made and new research directions have opened up.

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

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

Free noncommutative (nc) function theory is an analogue of classical function theory where one replaces functions between two complex vector spaces by functions between square matrices of all sizes over these vector spaces that respect matrix size, direct sums, and similarities. It has emerged in the last decade and a half as a vibrant research area with results that are sometimes similar to and sometimes strikingly different from the classical commutative setting, and with interconnections and applications ranging from free rings and free skew fields to free probability and random matrix theory to dimension independent linear matrix inequalities in systems and control. The purpose of this research in teams is to develop new relations between free probability and nc function theory by launching a systematic investigation and usage of asymptotic integration over classical compact matrix groups and their homogeneous spaces. We expect this to open the road for an asymptotic study of Hardy and Bergmann spaces of nc functions and exhibit completely new phenomena regarding Shilov boundaries and uniqueness sets in the nc setting.

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

This workshop aims at bringing together an interdisciplinary scientific community to share some of the state-of-the-art results in the theory of Herglotz-Nevanlinna functions, and to solve common open problems lying at the frontier of pure mathematics, applied mathematics, physics, and engineering. Further development of this theory would lead to significant progress not only in the area of pure mathematics, but also in its applications to antennas, metamaterials, and composite materials.

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

Higher-rank graphs generalize path categories of directed graphs and are intricately connected to various mathematical disciplines. This workshop aims to illuminate the rich interplay between higher-rank graph C*-algebras and fields such as algebra, theoretical physics, and geometry. By examining how these algebras both influence and are influenced by these diverse areas, the event will provide insights into their broader implications and applications. The workshop will bring together experts from different fields and career stages, each offering a unique perspective on higher-rank graphs. and interactions.

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

Institute for Computational and Experimental Research in Mathematics (ICERM)

This Semester Program will explore the emerging research field of Metric Algebraic Geometry, which is about the geometry induced by metric and probabilistic structures on sets defined by polynomial equations. The philosophy of this program is that regarding spaces and models as algebraic varieties opens up powerful – notably, global - approaches for problems involving distances and/or approximation. Instead of viewing spaces through local charts or via simplicial pieces, Metric Algebraic Geometry proposes finding global descriptions. This brings new computational tools to the table to establish strong theoretical properties over the geometric domain. Target applications include the nonlinear function spaces of neural networks, reduced-order models for large datasets, and configuration spaces of cameras or images in computer vision. The program will develop this area both within pure mathematics and in its applications. Activities will encourage experts in theoretical fields (such as algebraic geometry, differential geometry, and integral geometry) to commingle with experts in application-driven domains (like in machine learning, computer vision, optimization, nonlinear inverse problems and probabilistic modeling) and to all mentor the next generation. The results will set the research agenda for Metric Algebraic Geometry for years to come.

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

Algebraic distance optimization, a family of optimization problems defined by polynomial equations, is becoming a key approach for solving complex optimization tasks in computational algebraic geometry, computer graphics, image processing, and machine learning. Its primary focus is on solving algebraic optimization problems concerning the distance from a data point to a given algebraic variety. This workshop will bring together leading experts from algebraic geometry, algebraic statistics, optimization, and application areas to explore and develop advances in this research area.

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

Optimization

Institute for Computational and Experimental Research in Mathematics (ICERM)

Integral geometry is the subject of averaging geometric properties of a submanifold of a homogeneous space. This is a classical topic, with its origin in the so-called Buffon's needle problem: drop a random needle on a floor made of planks and calculate the probability the needle lies across a crack. This is solved formulating accurately what “random” means, so that expectations become integrals with respect to a certain measure (on the Grassmannian of lines in this case). Generalizations of this problem lead to beautiful progress in the theory of valuations on convex bodies and stochastic processes. In this workshop we will focus on more recent developments, especially on integral geometry of (real) algebraic varieties. This allows to establish connections with intersection theory and convex geometry. At the same time, restricting to the algebraic framework, opens the possibility of effective studies of average properties, with applications to sampling methods.

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

Institute for Computational and Experimental Research in Mathematics (ICERM)

The goal of this workshop is to deepen connections between algebraic geometry and data science. Behind many optimization methods is the modeling assumption that data lie on, or close to, an algebraic variety. We will discuss methods to sample from varieties or distributions centered on them, extending the methods to adaptive techniques and for sampling from level sets. We will investigate consequences and applications of these methods for computations in Bayesian statistics, likelihood inference, and topological data analysis. A complementary area of focus will be on learning functions and varieties from samples, and its uses to test goodness of fit, to investigate the geometric and topological structure of data, and for structured matrix and tensor decompositions. The workshop is at the interface of applied algebraic geometry with its applications in numerical computations, machine learning, and statistics. It will bring researchers from these communities together to learn from each other and exchange ideas.

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

Geometry and Topology,    Scientific Computing and Data Science

The Hausdorff Research Institute for Mathematics (HIM)

HIM School is a week-long event directed at PhD students and recent Postdocs.