Tom Mrowka (Massachusetts Institute of Technology)
Floer homology of three manifolds and applications to low dimensional topology abstract
Abstract:
Floer homology and the related invariants of 4-manifolds has given us deep insight in smooth differential topology in dimensions 3 and particularly 4. The theory has yielded insights like existence of exotic differentiable structures on 4 dimensional euclidean space, complex curves minimize genus in complex projective space, killing the Hauptvermuntung, there even appear to be connection to the 4 color map theorem. This course will build up Floer homology of three manifolds from scratch. The focus will be on Instanton Floer homology but we will mention other versions and develop applications as the course goes on.
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Gilbert Maystre
The Complexity of Two-Team Polymatrix Games with Independent Adversaries abstract
Abstract:
In a polymatrix team-game, players are grouped in teams so that any twoagents plays a coordination game if they are from the same team and azero-sum game if they are from different teams. It is known thatcomputing a Nash equilbrium is in CLS when there is only one team andalready as hard as general Nash equilibrium for three teams. In thistalk, we will explore the two-team case and show it is CLS-hard ingeneral and CLS-complete for the restricted setting of one team notcoordinating. This also has interesting implications on the complexityof solving some min-max formulations.
11:00 • EPF Lausanne, INJ114
Prof. Dr. Anton Khoroshkin (University of Haifa)
On Generating Series of Cohomology of Generalized Configuration Spaces abstract
Abstract:
A generalized configuration space on $X$ consists of a collection of points on $X$ with specific rules governing which points cannot coincide. In this work, I will introduce a new algebraic structure, called a "contractad," on the union of these spaces for $X = \\mathbb{R}^n$, which extends the concept of the little discs operad. I will demonstrate how this algebraic framework can be used to extract information regarding the Hilbert series of cohomology rings. Surprisingly, the same approach can be applied to generate series for various combinatorial data associated with graphs, such as the number of Hamiltonian paths, Hamiltonian cycles, acyclic orientations, and chromatic polynomials. Additionally, natural compactifications of these configuration spaces for $X = \\mathbb{C}$ generalize the Deligne-Mumford compactification of moduli spaces of rational curves with marked points. If time allows, we will also discuss the generating series for their cohomology. The talk is based on the joint work with D.Lyskov: https://arxiv.org/abs/2406.05909
13:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Remi Leclercq (Paris-Saclay University, Paris)
Local exactness of nearby Lagrangians and topological properties of orbits of Lagrangians abstract
Abstract:
The central point of this talk is to present a strategy for proving that Lagrangians which are displaceable by a Hamiltonian diffeomorphism admit a "Weinstein neighborhood of non-displacement", i.e. a neighborhood W of the given Lagrangian L such that if the image of L by a Hamiltonian diffeomorphism is included in W, it must intersect L. When the inclusion of L into M induces the 0-map at the level of first homology groups with real coefficients, this non-displacement property also holds for any Lagrangian included in W which is the image of L by a (non necessarily Hamiltonian) symplectomorphism. In both cases, non-displacement follows directly from "local exactness" of nearby Lagrangians, i.e. the fact that any Lagrangian in the Hamiltonian or symplectic orbit of L, included in W, is exact in W seen as a subset of T*L. I will give several natural examples for which such a neighborhood exists. I will then discuss applications of this line of ideas in terms of the topology of the Hamiltonian orbit of L, and in terms of C^0 symplectic geometry. This is joint work with Jean-Philippe Chassé.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Claire Burrin (University of Zurich)
Abstract:
I will discuss my current favorite illustration of the `unreasonable effectiveness\' of modular forms at the hand of the problem of quantifying the density of rational points on the sphere.
17:15 • Universität Bern, Sidlerstrasse 5, 3012 Bern, Room 228