Conferences  >  Mathematics  >  Geometry and Topology

The Hausdorff Research Institute for Mathematics (HIM)

Analytic questions of a discrete nature are ubiquitous in many areas of mathematics and theoretical computer science. The purpose of this conference is to bring together a diverse group of experts working, broadly, on Discrete Analysis with particular emphasis on questions having a geometric component. The topics will include Boolean analysis, vector-valued harmonic analysis, metric embeddings, geometry of graphs and groups, and aspects of discrete probability and theoretical computer science.

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.

Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups. These subgroups are central objects in the study of higher Teichmuller theory, convex projective geometry, and character varieties. In this summer school, there will be an emphasis on discussing some of the dynamical tools that have recently been successfully used to study Anosov subgroups. The required background in dynamics, hyperbolic geometry, and Lie theory will also be discussed. Aside from providing a stimulating academic environment for learning about Anosov subgroups, this summer school also aims to be a relaxed and friendly space for participants to interact with fellow aspiring mathematicians.

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

Organised in partnership with the Clay Mathematics Institute

Simons Laufer Mathematical Sciences Institute (SLMath)

This school will serve as an introduction to the SLMath semester “Topological and Geometric Structures in Low-Dimensions”. The school consists of two mini-courses: one on Teichmüller Theory and Hyperbolic 3-Manifolds and the other on Anosov Flows on Geometric 3-Manifolds. Both topics lie at the interface of low-dimensional geometric topology (specifically, surfaces, foliations, and 3-manifolds) and low-dimensional dynamics. The first course will be targeted towards students who have completed the standard first year graduate courses in geometry, topology, and analysis while the second course will geared towards more advanced students who are closer to beginning research. However, we expect that all students will benefit from both courses.

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

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

The Fields Institute for Research in Mathematical Sciences

Group theory and topology have a long and rich history of interaction. This workshop will bring together experts working on different aspects of this interaction in order to share ideas and boost the development of new methods that can be applied to the topology of configuration spaces, braid groups, mapping class groups and manifolds, and spaces of commuting elements.

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

The Summer school: "Invitation to complex geometry" will be held between 04-08 August 2025 at the main lecture hall of the Rényi Institute (Budapest) as part of the thematic semester Complex analysis and Geometry (August-December 2025) hosted by the Erdős center. Graduate students (Msc and PhD), postdocs, and early career researchers are encouraged to apply.

The conference brings together experts from related fields, such as Riemannian geometry, dynamical systems, algebraic geometry, symplectic geometry, PDEs and mathematical physics, exchanging ideas and sharing methods of study of different problems in integrable systems, applying these ideas and methods in their respective research projects. Synergy effect is expected, and indeed, was demonstrated in earlier editions of the conference.

American Institute of Mathematics, Pasadena, California (AIM)

The "Summer school on singular Kählerian metrics and Hermitian geometry" will be held between 11-15 August 2025, at the main lecture hall of the Rényi Institute (Budapest), as part of the thematic semester Complex analysis and Geometry (August-December 2025) hosted by the Erdős center. Advanced PhD students , postdocs, and junior researchers working in complex geometry are encouraged to apply. During this one week summer school, Hans-Joachim Hein (Münster) and Daniele Angella (Firenze) will give series of talks on recent advances on singular Kähler metrics, and Hermitian geometry respectively. We expect that the audience will consist of advanced graduate students, postdocs and junior faculty working in complex geometry.

The René 25 conference will bring together renowned international researchers in mathematics to celebrate the research interests of René Schoof, which include the fields of algebraic number theory, arithmetic algebraic geometry, computational number theory and coding theory.

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to studying a nascent bridge between commutative algebra and symplectic geometry, with an emphasis on developing Macaulay2 software for homological computations at the interface of these two fields. Recent breakthrough work of Hanlon-Hicks-Lazarev and Favero-Huang employs symplectic techniques to build line bundle resolutions over toric varieties, resolving several conjectures in toric geometry and multigraded commutative algebra. These results have illuminated a striking new connection between commutative algebra and symplectic geometry: this workshop will bring together experts in these fields with the goal of increasing our computational power to study the interplay between them.

The Institute for Mathematical and Statistical Innovation (IMSI)

This week-long conference is in celebration of the 10-year anniversary of AATRN, the Applied Algebraic Topology Research Network. It will be the first time that AATRN meets in person, bringing together researchers from different backgrounds—mathematics, statistics, computer science, physics, biology, etc. In other words, AATRN will be “geometrically realized” at the Institute for Mathematical and Statistical Innovation in Chicago, USA!

Algebra,    Meetings of Professional Bodies in Mathematics

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

Neural Networks and Artificial Intelligence, Machine Learning,    Optimization Theory, Operational Research

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

This program will focus on several aspects of the theory of automorphic forms with an emphasis on the relations among the internal structure of spaces of automorphic forms, the Langlands functoriality principle, automorphic L-functions, and questions in geometry, in particular, those regarding locally symmetric spaces. These are associated with arithmetic subgroups of a given reductive algebraic group G dened over analgebraic number field. Special attention is given to the theory of Eisenstein series and their ubiquitous role within the theory of automorphic forms.

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

The aim of this workshop is to explore recent advances in Kähler geometry, focusing on non-Archimedean aspects of the Strominger--Yau--Zaslow conjecture, potential-theoretic approaches to singular Kähler-Einstein metrics, geometric estimates for solutions to Complex Monge–Ampère equations, connections with the minimal model program, and Calabi-Yau metrics on non-compact manifolds.

Mathematical Logic and Foundations,    Courses and Events for Math Students and Early Career Researchers

This conference aims to honor the spectacular contributions of Emmanuel Ullmo to arithmetic geometry and centers around his mathematical contributions and interests. It will cover and highlight recent stage of development on topics such as Diophantine geometry, ergodic theory, Hodge theory, and arithmetic dynamics.

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.

Banach Center

Analysis,    Probability and Statistics, Game Theory

Mathematical Institute SANU

This workshop convenes researchers working at the intersection of topology, geometry, probability, and stochastic processes to exchange recent advances and foster discussions on their wide-ranging applications.

Geometry, Stochastic, Algebraic Topology, Persistent Homology, Probabilistic topology

The summer school is about formulas of Siegel and Weil and its impact in the theory of sphere packings, number theory, and geometry. The summer school takes place at Bielefed University.

Number Theory, Arithmetic,    Courses and Events for Math Students and Early Career Researchers

Rutgers University, Newark

The focus of the workshop is the interactions of 3-manifold topology and geometry, and the study of 3-manifold groups and character and representation varieties with computational topology and theoretical computer science. We also welcome related topics! There will be several introductory lectures and longer research talks, and some short (lightning) talks. There also will be ample time for discussions and informal interactions.

American Mathematical Society

This 2-day special session will be dedicated to a range of mathematical problems related to motion planning algorithms and their properties. A central role is played by the notion of topological complexity (TC), which is a homotopy invariant depending only on the configuration space of the robot that can be studied using diverse tools from a variety of fields, such as geometry, topology, algebra, combinatorics, etc. This session will include talks on a variety of topics from algebraic topology, geometric topology, and topological robotics, though most will focus on (sequential) topological complexity, Lusternik–Schnirelmann category, robot motion planning problems, and homotopy invariants related to (or analogous to) sectional category. The session aims to bring together scientists from all over the world working on different aspects of motion planning and TC and foster collaboration among them, expose graduate students and junior colleagues to these rich and fascinating areas of research, and identify directions for future work and interaction in these areas.

Event Organizer;     Email: ekanshjauhari@ufl.edu

topological complexity, LS-category, sectional category, motion planning, robotics, applied algebraic topology

Algebra,    Systems theory, Control and Automation

Galician Center for Mathematical Research and Technology (CITMAga) - University of Santiago de Compostela (USC)

The aim of this conference is to gather experts in the study of symmetry in Differential Geometry, whilst we celebrate Carlos E. Olmos' 65th birthday. The conference will revolve around the study of curvature, homogeneous and symmetric spaces, Riemannian submanifold geometry, holonomy, and other related topics in Differential Geometry and Geometric Analysis.

Email: congreso.symmetry2025@usc.gal

Differential geometry, Riemannian geometry, geometric analysis, submanifold geometry, holonomy, homogeneous spaces, symmetric spaces, curvature

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to studying arithmetic dynamics of multiple maps. In classical arithmetic dynamics, we consider the iteration of a single endomorphism of a variety defined over a field of arithmetic interest — typically a number field or the function field of a curve. An exciting new direction in arithmetic dynamics that holds particular promise for striking new results is what we call "dynamics of multiple maps": dynamical behavior arising from the interaction of two or more endomorphisms on the same space. This includes iteratively applying rational functions on P1 chosen at random from a family according to some probability distribution; a correspondence from a variety X to itself; and forming words from a non-commuting family of involutions on a K3-surface.

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to non-Archimedean methods in complex geometry.

The International Centre for Mathematical Sciences (ICMS)

The interplay between geometry and physics has been a driving force for new developments in both mathematics and physics for a very long time. In the last two decades, higher category theory has become a fine contributor in this dialogue, providing many invaluable ideas and very useful heuristics. Organised in partnership with the Clay Mathematics Institute, this workshop aims to present the latest results in the application of (higher) geometry to theoretical physics and to foster new collaborations between mathematicians and theoretical physicists.

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

This workshop will bring together researchers working on two fields seemingly at odds, and incompatible: combinatorial geometry and uncertainty. Combinatorial geometry is a field of counting discrete objects, it is about how things are connected, or in general how discrete objects like points, lines, and circles intersect with each other. On the other hand, modeling uncertainty is about not allowing discrete events to happen precisely, or at least not with confidence. It replaces these notions with probabilistic concepts. How can one count geometric objects and their connectivity properties if there is uncertainty in their very existence?

Graph Theory and Combinatorics,    Probability and Statistics, Game Theory

Isaac Newton Institute for Mathematical Sciences

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

Mathematicians have been studying notions of space and geometry for thousands of years. Over time our models for spaces have grown successively more abstract. A major conceptual leap in the 1960's was taken with the theory of algebraic stacks, which are a sort of space with "internal symmetries'' not visible in usual geometric objects. There has been a flurry of recent activity among mathematical researchers in understanding the structure of these spaces. This workshop will bring together researchers developing this state-of-the-art theory with mathematicians at various career stages who are interested in applying this theory in their work. The organizers hope that this week of focused discussion on this topic will help bring these methods to a wider audience and lead to significant new developments both in the foundations of the theory and in applications.

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.

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

Hyperbolic spaces and, in particular, a generalization called asymptotically hyperbolic spaces, have in recent decades been the focus of intense mathematical interest. They have surprising applications in the physics of string theory and are important for the study of isolated systems in the theory of general relativity. The closely related de Sitter and anti-de Sitter spaces also arise in the study of cosmology. The purpose of this workshop is to bring together established experts and emerging new talents in the field who study diverse aspects of these fascinating objects. We will discuss some of the remarkable recent developments in the geometric analysis of these spaces, including developments in inverse problems, the various meanings of mass-energy in this setting, the interaction between the mathematical developments and physics, and new ideas to extend the theory beyond the asymptotically hyperbolic setting.

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.

Algebra,    Graph Theory and Combinatorics

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

The study of geometric properties of convex bodies based on information about sections or projections of these bodies belongs to the area of geometric tomography and has important applications to many areas of mathematics and science, in general. In recent years, there has been a significant increase in the interaction between harmonic analysis and convex geometry, leading to solutions for several longstanding open problems, the discovery of new phenomena, and many new intriguing open questions. The goal of this workshop is to bring together young and established researchers to discuss recent developments and advance applications of harmonic analysis to convex geometry and geometric tomography.

Analysis,    Calculus, Differential Equations and Integration

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

A team of three leading experts in algebraic and quantum geometry will convene at the Banff International Research Station (BIRS) to tackle a longstanding conjecture on the classification of vector bundles on the quantum projective line. Their collaboration aims to bridge the gap between classical algebraic geometry and emerging structures in quantum geometry, advancing our understanding of noncommutative spaces. The classification of vector bundles has been a cornerstone of modern algebraic geometry, with the celebrated Grothendieck’s Theorem providing a complete classification of vector bundles over the classical projective line. However, the quantum analog remains an open problem, representing a major challenge in the study of noncommutative algebraic geometry. A positive solution to the conjecture under investigation would significantly advance the field, providing new insights into the structure of quantum projective spaces and their applications in both mathematics and theoretical physics.

Mathematical Physics,    Quantum Mechanics and Quantum Technology

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.

Algebra,    Graph Theory and Combinatorics

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

This event will facilitate a broad overview of the state of the art in quantum invariants, including fast computations, universal invariants and their relationships to famous equations arising from quantum physics and algebra, and the interplay between topological and geometric properties of spaces. The participant list features many of the leading world experts in this area, and provides opportunities for young researchers to become involved through an early career showcase, problem sessions, mentoring, and informal interactions.

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

The goal is to bring together researchers of different experience levels, from advanced graduate students to established mathematicians, in order to jointly work on research projects on topics of common interest within Toric Topology and Polyhedral Products. The focus of the workshop will be on active collaboration in teams, and while the weeklong workshop will be the most condensed part of the collaboration, it is expected that a significant amount of work on the projects will be done before as well as after the workshop. It is expected that at least one research paper be produced from each collaboration which will be published in a workshop proceedings after obtaining referees' approval.

On the occasion of 40+ years after the seminar paper of Gross--Zagier, we bring together experts to deliver lectures on a broad range of topics connected with the Gross-Zagier formula, its generalizations, related future directions, and other works that it has inspired.

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,    Algebra

The program will unite researchers from a number of areas: algebraic and complex geometry, arithmetic geometry, Hodge theory, and mathematical physics. It will bring theoretically and computationally oriented researchers together, expecting that computations will illuminate conjectures made by the theorists and that theory will enlarge the range of what can be computed. We intend to develop databases of certain types of K3 surfaces for the L-Functions and Modular Forms Database and promote the development of software for computations on K3 surfaces in Magma, SageMath, or other systems for public release.

Number Theory, Arithmetic,    Courses and Events for Math Students and Early Career Researchers