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CIRM – Centre International de Rencontres Mathématiques

The main goal of these Etats de la recherche is to review some of the most recent spectacular developments in algebraic, analytic and arithmetic dynamics. Covered themes will include a variety of problems related to the iteration of rational maps on algebraic varieties as well as the study of their dynamical moduli spaces. Depending on the structure of the ambient field over which these maps are defined, methods may vary drastically. Over the field of complex numbers, one speaks of holomorphic dynamics in which quasi-conformal deformations play a key role. The case of maps defined over general metrized fields have led to the developments of dynamics over Berkovich spaces. One can also consider maps over number fields whose study lies at the core of arithmetic dynamics. Interactions between these various fields have deepened in the recent years. Complex pluripotential theory combined with tools from arithmetic geometry has been used to prove equidistribution results with applications to problems of unlikely intersection, and to explore dynamical moduli spaces and their special varieties. Methods in p-adic analysis and from the minimal model program have revolutionized our understanding of groups of birational transformations. Non-archimedean dynamics has been turned into a very efficient tool to analyze degeneration problems in holomorphic dynamics.

Kurse und Veranstaltungen für Studenten der Mathematik,    Analysis

CIRM – Centre International de Rencontres Mathématiques

This Thematic Month aims to cover topics related to singularity theory of algebraic or analytic spaces, algebraic study of differential equations, and their applications to questions of transcendence. This 5-week program covers different themes that are often not closely related. One of the main objectives is to make them interact. To encourage participants (especially the youngest ones) to attend the entire month and foster interactions outside each one’s expertise zone, the scientific program of each week of the month will consist of courses accessible to non-experts, as well as more specialized presentations.

Department of Pure Mathematics, University of Calcutta, India

International Conference on Pure Mathematics and its Applications (ICPMA-2025) aims to bring together several leading academicians and researchers from different corners of the world to exchange their knowledge and share their research outcomes. This conference intends to provide a platform, particularly for young researchers, to learn from the veterans and rejuvenate through the academic discussions with the experts of various fields of mathematics.

Convenor or Jt. Convenor;     Email: cupuremathseminar@caluniv.ac.in

Algebra, Differential Equations, Dynamical Systems and Nonlinear Analysis, Functional Analysis, Geometry and Topology, Graph Theory, Harmonic Analysis, Mathematical Logic, Measure Theory, Number Theory and Cryptography, Real and Complex Analysis.

Geometrie und Topologie,    Graphentheorie und Kombinatorik

This meeting is dedicated to the memory of Heinz Langer, who unexpectedly passed away on 25th January 2024 in the eighty-ninth year of his life. The intention is to gather friends and colleagues and keep alive the memories of Heinz -- as a person and as a scientist.

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.

Graphentheorie und Kombinatorik,    Numerische Analysis

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Graphentheorie und Kombinatorik,    Statistik, Spieltheorie

CIRM – Centre International de Rencontres Mathématiques

Starting in the 2011 Annals of Mathematics paper of Foreman, Rudolph and Weiss there have many results showing that classical problems in dynamical systems are unsolvable using inherently countable resources. The initial results were for abstract measure preserving systems, but more recent work has focussed on smooth systems on compact manifolds. Gerber and Kunde have made very significant contributions for smooth transformations that are weakly mixing and for Kautomorphisms. They also showed that the Kakutani equivalence relation is not Borel. These results raise more questions than they solve! The proposed Research inResidence is to bring the four researchers together to share knowledge and techniques and hopefully make progress on the open problems.

CIRM – Centre International de Rencontres Mathématiques

K-stability is a central topic in modern complex geometry. It characterises Fano manifolds that admit a Kähler-Einstein metric and provides a good notion of compact moduli space for Fano varieties. The winter school will bring together experts on K-stability who will give 8 mini-courses for PhD students and young researchers with a special focus on explicit problems in dimensions two and three. Along with lecture courses, there will be exercise sessions.

CIRM – Centre International de Rencontres Mathématiques

We plan to work on several explicit problems about K-stability of smooth and singular Fano threefolds described in the proposal together with Hamid Abban (Nottingham, England) and Kento Fujita (Osaka, Japan). Hamid Abban works on K-stability of Fano varieites, and birational geometry of Fano varieties. His recent results on K-stability crucially changed the subject over the last two years. Kento Fujita is an expert in the general theory of K-stability of Fano varieties. One of the most important works of Fujita consisted on finding and proving a valuative criterion for K-stability.

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Faculty of Mathematics at the Universität Regensburg

Geometrie und Topologie,    Analysis

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

Graphentheorie und Kombinatorik,    Analysis

Harmonic analysis on homogeneous spaces is a fundamental area of research that simultaneously generalizes classical harmonic analysis on groups and on Riemannian symmetric spaces. It naturally relates to many areas of mathematics, playing a central role in representation theory and the theory of automorphic forms.

Representation Theory and Noncommutative Geometry

Analysis,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

Isaac Newton Institute for Mathematical Sciences

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

CIRM – Centre International de Rencontres Mathématiques

During the past decades, Teichmüller–Thurston theory and its connections to geometrization of 3-manifolds have been used as a model to understand discrete subgroups of higher rank Lie groups and their associated locally homogeneous manifolds. This lead to spectacular developments in which the notion of Anosov group (a subtle higher rank generalization of convex-cocompactness) plays a central role. This school, aimed primarily at PhD students and young postdocs, will present the fundamental results on which these recent developments build, including both geometric, dynamical and analytic aspects of discrete subgroups of Lie groups.

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

This workshop is devoted to interactions between continued fraction algorithms (in dimension one and mostly higher) and arithmetic, automatic and uniformly distributed sequences. Problems in this area inspired a lot of work in dynamical systems in general, and the techniques that were developed over the years found applications well beyond their original motivation. Milestones in the theory were achieved by Austrian and Dutch mathematicians and collaborations between them: Hlawka-Koksma and Kuipers-Niederreiter.

Mathematische Logik, Grundlagen der Mathematik,    Graphentheorie und Kombinatorik

CIRM – Centre International de Rencontres Mathématiques

Friezes, introduced 50 years ago by Coxeter, are patterns of integers defined by a simple, local condition. They consist of a finite (or infinite) number of rows written in a lattice, starting with a row of 0s and a row of 1s and satisfying a local SL2-rule: for any four neighbours a, b, c, d forming a diamond we require ad − bc = 1. Since the discovery of links to cluster algebras of type A, a plethora of generalisations have been studied in the last decades. With this workshop, we will provide a platform to establish new links between friezes and research areas in geometry, algebra and combinatorics.

Geometrie und Topologie,    Graphentheorie und Kombinatorik

Isaac Newton Institute for Mathematical Sciences

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

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

The purpose of the workshop is to bring together researchers and students interested in design theory, especially as it relates to Hadamard matrices and their applications, as well as in related areas in coding theory, association schemes, sequences, finite geometry, difference sets, quantum information theory, theoretical physics and computer security. The audiences would learn about the latest developments in these areas, discuss the latest findings, take stock of what remains to be done on classical problems and explore different visions for setting the direction for future work.

Banach Center

The University of Sydney and Sydney Mathematical Research Institute

The conference will bring together experts in representation theory and algebraic combinatorics, and is part of a broader special semester on "Modern Perspectives in Representation Theory" at the Sydney Mathematical Research Institute, running from May 5 to June 13, 2025.

Any of the organizers: Charlotte Chan, Thomas Lam, Andrew Mathas, Dani Tubbenhauer, Geordie Williamson

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

Banach Center

The conference will explore the Yang-Baxter equation (YBE), a central topic in pure mathematics with connections to particle physics, statistical mechanics, and various mathematical fields like algebra, knot theory, tensor categories, and Hopf–Galois theory. Introduced in the 1960s by Yang and Baxter, the YBE has evolved into a rich and profound area of study. Drinfel'd's combinatorial version of the YBE, proposed in 1992, unveiled deep connections to numerous mathematical structures, including skew polynomial algebras, Bieberbach and Garside groups, and self-distributive structures such as racks and quandles. New algebraic concepts such as cycle sets, braces, and trusses were developed to address YBE-related problems and have found applications in other areas of mathematics.

Isaac Newton Institute for Mathematical Sciences

Equivariant homotopy theory in context

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Centre International de Rencontres Mathématiques (CIRM)

International Linear Algebra Society (ILAS)

Linear algebra, a fundamental subject in mathematics, boasts a multitude of applications across various domains. The theory of positive definite matrices, for instance, plays a pivotal role in operator theory and quantum information. Matrix decompositions offer essential tools for image processing, noise reduction, and data science. Combinatorial matrix theory has deepened connections between graph theory, enumeration, and matrix theory. More than these, linear algebra finds its presence in numerous disciplines and remains an active area of research.

In recent years, there has been an explosion of activity surrounding algebraic points on curves, from many different perspectives. These include the study of measures of irrationality, isolated and parametrized points, computational methods to determine algebraic points, and the arithmetic statistics of algebraic points. In this workshop, we aim to bring together researchers from these diverse perspectives, with the particular goal of developing bridges between them. The workshop will include overview talks on the various perspectives, research talks, an open problem session, and structured time for collaboration.

Zahlentheorie, Arithmetik,    Geometrie und Topologie

Join us for the 2025 Conference on Theoretical and Computational Algebra, from 29 June to 3 July, at the University of Évora, Portugal — a historic city in the heart of the beautiful Alentejo region. This year, we celebrate Peter Cameron’s remarkable contributions to groups, semigroups, combinatorics, statistics — and beyond!

Groups, Semigroups, Combinatorics, Computation

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.

Banach Center

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

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

We will gather to celebrate and showcase the spectacular advances in algebraic number theory and arithmetic geometry inspired by the vast research program of Henri Darmon.

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

The goal of this workshop is to bring together both senior and junior specialists in the fields of almost complex and non-Kähler geometry to present their latest achievements in research. Key topics will include cohomological properties of complex and symplectic manifolds, analytical techniques in non-Kähler geometry, special structures on complex manifolds, deformations of complex objects, topological aspects of complex and symplectic manifolds, and Hodge theory on almost Hermitian manifolds.

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

Banach Center

Since its origins in the work of Sophus Lie (now more than a century ago), Lie theory has seen tremendous developments and is now fundamental in many areas of mathematics (like group theory, geometry, symmetric spaces etc) and physics (quantum mechanics, particle physics, theory of gravity). Nowadays there are specialized computer packages such as LiE, the Atlas project, the package Chevie for GAP3, the program ChevLie. Also the more general purpose computer algebra systems GAP4, MAGMA and SageMath have large libraries for dealing with various objects that are central to Lie theory.

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.

Graphentheorie und Kombinatorik,    Geometrie und Topologie