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Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

The Fields Institute

This conference is intended to provide an overview of current research in homotopy theory, which has vastly expanded since its roots in the 19th century from the study of topological spaces by algebraic and combinatorial means to other fields of mathematics, including algebraic geometry, differential topology, and mathematical physics.

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

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

Graphentheorie und Kombinatorik,    Gruppentheorie

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

Watanabe's work on embedding calculus has shown us how diffeomorphisms of the 4-sphere may be studied, and Zemke's work has used the functoriality of Floer homology to derive powerful new obstructions to ribbon concordance. A common theme in these works is the emphasis on functoriality of the invariants, rather than simply computation, and a renewed interest in understanding diffeomorphism groups of a manifold rather than single isotopy groups. In this workshop, we propose to bring together experts on these interrelated topics with the aim of improving community understanding of recent developments in low-dimensional topology and promote new advances in the study of global properties of 4-manifolds.

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

The goal of this workshop is to create an opportunity for researchers in low-dimensional topology to encounter new research in the area, to establish new collaborations and reestablish existing ones, and to compensate for the relative isolation inflicted by the Covid-19 pandemic. One particular goal is to help researchers at earlier stages of their career to form connections, as these people were heavily affected by travel restrictions in 2020-21 and an inability to build networks. Together, ju- nior and senior researchers will exchange techniques, attack outstanding conjectures, and develop new directions of study.

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

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

This is a workshop in commutative algebra, broadly interpreted, with a focus on three areas, all concerned with resolutions in various forms. One is the resolution of singularities of algebraic varieties, which remains a vibrant topic of research. The second is the theory of noncommutative resolution of singularities. Introduced two decades ago, this subject has witnessed remarkable growth developing connections to algebraic geometry, commutative algebra, cluster algebras, and the representation theory of algebras, both commutative and noncommutative, among others. The third intended meaning of the word “resolution” is as in free resolutions of algebras and modules in commutative algebra.

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

Families of p-adic automorphic forms are well studied objects of arithmetic geometry since the pioneering work of Hida and Coleman. Their study resulted in the definition of geometric objects, called eigenvarieties, that parametrize systems of Hecke eigenvalues of p-adic automorphic forms. Conversely, the rich geometry of these varieties gives insights about p-adic (and thereby also about classical) automorphic forms. Recent techniques from perfectoid geometry, locally analytic representation theory and the point of view of the p-adic Langlands program give new insights and impulses. The spring school will give an introduction to both p-adic automorphic forms and eigenvarieties as well as the necessary background in p-adic analytic geometry. The courses will be complemented by research talks that will focus on recent developments in the area.

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

A conference in memory of Claus-Günther Schmidt.

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

This workshop focuses on interactions between real algebraic geometry, operator theory, and optimization, with a particular emphasis on the interrelations with the Koopman operator approach to optimization and control. It is an outgrowth of three previous successful MFO workshops held in 2014, 2017, and 2020, themselves a continuation of a long series of MFO workshops on real algebraic geometry which started in 1984. The mathematical topics of interest include sum-of-squares representations of non-negative polynomials in commutative and non-commutative algebras and the dual problem of moments, including various applications, and the use of linear infinite dimensional methods in nonlinear dynamical systems.

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

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

The Arbeitsgemeinschaft (study group) mainly addresses to non-specialists who want to broaden their outlook on mathematics and to junior mathematicians who wish to enter a field for future research. Experts are also welcome. The idea is “learning by doing” – similar to the Seminaire Bourbaki. Participants have to volunteer for one of the lectures described in the program of the Arbeitsgemeinschaft. After the deadline for application the organizers choose the actual speakers to give them enough time to understand the subject and to prepare for their lectures.

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

Hausdorff Center for Mathematic

This conference will be on various aspects of the local Langlands correspondence over p-adic fields and methods from p-adic Hodge theory. Topics will include the usual local Langlands correspondence, the p-adic local Langlands correspondence and the relation to coherent sheaves on spaces of Galois representations, and the geometry and cohomology of local Shimura varieties.

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

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

In the tradition of the earlier events, this workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety does have any rational point at all.

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

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

Hausdorff Center for Mathematic

This conference will be on various aspects of the global Langlands correspondence. Topics will include in particular the geometry and cohomology of Shimura varieties and more general locally symmetric spaces, or moduli spaces of shtukas.

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

The conference is about recent developments in Arithmetic Algebraic Geometry. Its central theme is the geometry of Shimura varieties and related spaces in all its facets. Topics to be covered include: Integral models of Shimura varieties and the geometry of their reductions, p-adic and perfectoid geometry, special cycles on Shimura varieties, moduli spaces of Galois representations and (φ, Γ)-modules.

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

Geometrie und Topologie,    Graphentheorie und Kombinatorik