Konferenzen  >  Mathematik  >  Geometrie und Topologie

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.

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?

Graphentheorie und Kombinatorik,    Statistik, Spieltheorie

Isaac Newton Institute for Mathematical Sciences

Jagiellonian University, Faculty of Mathematics and Computer Science

Probabilistic methods were pioneered in combinatorics, often providing the first constructions of interesting classes of objects. We are now at a point where these methods evolved to yield important new examples in Riemannian geometry and dynamics. On the other side, ergodic methods were for a long time used to prove rigidity theorems in Riemannian geometry, a trend that continues to this day. Sometimes these two approaches can be fruitfully combined. The goal of this meeting is to explore interactions of probabilistic and ergodic methods in broadly understood geometry.

Organiser email;     Email: pierogy@matinf.uj.edu.pl

probabilistic notions of convergence of actions, random subgroups, random manifolds, geometric group theory, ergodic theory, measurable actions, measurable equivalence relations, percolation on graphs, stochastic geometry

Statistik, Spieltheorie ,    Gruppentheorie

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.

Fulbright College of Arts & Sciences, Department of Mathematical Sciences, University of Arkansas

The Arkansas Spring Lecture Series in the Mathematical Sciences are research conferences focused on a specific topic chosen among the current leading research areas. A principal lecturer is invited to deliver a five-lectures course, and a few specialists give talks on subjects closely related to the conference main topic. Short talks by young Ph.D.s and finishing graduate students are solicited to complement the conference.

Fulbright College of Arts & Sciences, Department of Mathematical Sciences, University of Arkansas

Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH

The mathematical study of fundamental objects such as curves, embedded graphs, surfaces, and 3-manifolds has a rich and old history. However, the study of their algorithmic and combinatorial properties and the underlying computational questions is still in its infancy. There is a diverse pool of open problems and unanswered questions from the complexity- theoretic side. Examples include the hardness of realizability, the fine-grained complexity of distance and similarity measure computations, the existence of polynomial-time algorithms for flip distances, or the approximability of such distances. When dealing with polyhedral structures associated with geometric or topological objects, methods from Combinatorics and Algebra come into play to analyze structures such as associahedra, secondary polytopes, and mapping class groups of surfaces. Applied fields such as trajectory analysis and machine learning bring new questions and a fresh perspective to the field. This Dagstuhl Seminar on intractability in discrete geometry and topology will bring together researchers from the fields of computational complexity, computational geometry, topology, discrete geometry, and graph drawing; and will focus on the algorithmic, combinatorial, and computational questions mentioned above.

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.

American Mathematical Society and Georgia Southern University-Armstrong Campus

The interaction between topology and curvature is a fundamental theme in modern mathematics. The study of scalar curvature plays an increasingly important role not only in geometry and topology, but also in general relativity and theoretical physics more generally through the theory of Dirac operators. This special session will bring together experts and young researchers who study these topics from many different points of view. The aim of this session is to share viewpoints and progress on understanding the scalar curvature and topology of manifolds, and to establish new connections among the culturally diverse groups spread worldwide, but particularly in the USA.

Email: ekanshjauhari@ufl.edu

Global Riemannian geometry, curvature restrictions, differential geometric analysis, index theory, spin geometry, algebraic topology of manifolds.

Mathematische Physik,    Analysis

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,    Graphentheorie und Kombinatorik

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,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

Institute for Computational and Experimental Research in Mathematics

Geometric and topological methods are reshaping the study of complex, high-dimensional data, yet their theoretical foundations still lag behind their accelerating adoption in practice. This workshop will bring together researchers in computational geometry, applied topology, and machine learning to fortify and extend these foundations while developing scalable, interpretable approaches for data-driven science. By bridging theory and computation, the program aims to clarify core principles, overcome algorithmic bottlenecks, and establish rigorous frameworks that can guide future applications. The workshop will feature talks from senior leaders and rising scholars, collaborative discussions, and opportunities for junior participants to engage with the community and help shape the evolving landscape of the field.

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

Institute for Computational and Experimental Research in Mathematics

Spheres are the basic building blocks of geometry. More complicated geometric objects can be built by attaching spheres to each other along continuous maps. For many purposes, such constructions depend only on the homotopy classes of these continuous maps. A fundamental problem in algebraic topology is to compute these homotopy classes, i.e., to compute the homotopy groups of spheres. Machines can be used to great effect in the exhaustive computation of these fundamental invariants of homotopy theory. The workshop will study several software packages that are specifically designed for this purpose. Participants will have the opportunity to interact directly with codebases in work groups led by experienced programmers. The workshop will also introduce a variety of projects in homotopy theory that rely on computers.

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

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.

Mathematische Physik,    Quantenmechanik und Quantentechnologie

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,    Graphentheorie und Kombinatorik

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.

Institute for Computational and Experimental Research in Mathematics

This workshop will explore the rich and rapidly evolving interface between high-dimensional geometry, probability, and computational methods. Recent years have witnessed major break-throughs, bringing tools from stochastic processes to resolve long-standing problems in geometry, and using geometry to investigate the limits of computation and efficiency of sampling algorithms.

The workshop will bring together researchers from the communities of geometry, probability, and computational complexity to promote further synergy and continue the progress on the major open problems of the field.

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

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.

Graphentheorie und Kombinatorik,    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.

Zahlentheorie, Arithmetik,    Kurse und Veranstaltungen für Studenten der Mathematik

Institute for Computational and Experimental Research in Mathematics

Cubic fourfolds and Gushel-Mukai fourfolds are bound to K3 surfaces through geometry and Hodge theory; when they contain unexpected surfaces, their middle cohomology contains a Hodge structure matching that of a K3 surface. This association contains rich geometry and involves certain Hyperkähler manifolds associated to the cubic fourfold. Hyperkähler manifolds are higher-dimensional generalizations of K3 surfaces, whose second cohomology group with integer coefficients has a lattice structure that allows us to study them with tools analogous to those used to understand K3 surfaces. The past 30 years have seen significant advances and new avenues develop in the study of the geometry of cubic fourfolds, Gushel-Mukai fourfolds, and high-dimensional Hyperkähler manifolds. The aim of this workshop is to bring together experts from algebraic and arithmetic geometry to exchange mutually beneficial points of view. For example, are there computations over finite fields that could inform or lead to a Honda-Tate theory for K3 surfaces? Are there exotic automorphism groups of high-dimensional Hyperkähler manifolds in positive characteristic? What geometric insights can be descended to number fields for applications to the study of rational points and the Brauer-Manin obstruction? We hope to study these and many other similar questions.

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

Institute for Computational and Experimental Research in Mathematics

Moduli spaces of K3 surfaces can be constructed using many points of view in algebraic geometry, including Hodge theory, birational geometry, and invariant theory. These different perspectives often yield related but distinct compactifications of the moduli of K3 surfaces. The current understanding of these spaces is quite explicit for low degree polarized K3 surfaces but requires a significant increase in computational complexity in higher degrees. Furthermore, studying moduli of K3 surfaces informs the study of moduli of other K-trivial varieties, such as abelian varieties and Calabi-Yau manifolds, related to many open questions in algebraic geometry. The goal of this workshop is to explore connections between different perspectives on moduli of K3 surfaces and applications to other K-trivial varieties. This workshop intends to unite experts in Hodge theory, birational geometry and moduli of Calabi Yau manifolds, singularity theory, mirror symmetry, and anyone working on questions related to degenerations and deformations of K3 surfaces.

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