Javier de la Bodega-Aldama (KU Leuven)
The arc-Floer conjecture: from arithmetic to symplectic topology abstract
Abstract:
In the same philosophy as the Weil conjectures, Igusa\'s classical monodromy conjecture suggests a mysterious connection between the arithmetic and the topology of hypersurface singularities. Although it has been verified in several cases, the conjecture is still widely open, and the attempts to solve it have motivated new developments in different directions: motivic, nonarchimedean, model-theoretic, etc. In 2022, Budur, F. de Bobadilla, Lê and Nguyen suggested a new approach by exploding the symplectic properties of the Milnor fibration.More precisely, the authors suggested the so-called arc-Floer conjecture, which states that the cohomology of contact loci coincides (up to a shift) with the Floer homology of the iterates of a symplectic monodromy. However, the authors formulated the conjecture based on analogies but not on actual evidence. In 2023, de la Bodega and de Lorenzo Poza verified it for plane curve singularities, providing the first piece of evidence supporting the arc-Floer conjecture. In this talk, we will give an overview of the problem and explain the proof for plane curves.
10:15 • EPF Lausanne
Julia Münch (University of Liverpool)
Abstract:
Uniformly quasi-regular maps are a suitable class to study in order to extend the concepts and ideas of complex dynamics to non-holomorphic functions. The dynamics of quasi-regular mappings are particularly interesting in R^n for n equal to at least 3. However it is not easy to find non-trivial examples of uniformly quasi-regular maps. In the talk I will present how one can extend any rational expanding Thurston map f defined on the Riemann sphere to a map F defined on an open neighbourhood Ω containing S^2. The map is uniformly quasi-regular as long as the iteration is defined. In a second part I will talk about properties of the extension with respect to the Poincare metric on the unit ball. I will show how to find a quasi-isometric embedding of the hyperbolic plane into B(0,1) arising from the dynamics of f on the sphere. This is work in progress.
Prof. Dr. Michael Hochman (The Hebrew University of Jerusalem)
New results on embedding and intersections of self-similar sets abstract
Abstract:
I will discuss the problem of affinely embedding self-similar sets in the line into other such sets. Conjecturally, embedding is precluded when the contraction ratios of the defining maps are incommensurable. This is closely related to conjectures on intersections of fractals, but in the open cases even the embedding problem is challenging. I will describe recent joint work with Amir Algom and Meng Wu in which we confirm the conjecture whenever the contraction ratios are algebraic numbers, and also for a.e. choice of parameters. I will discuss the proof. If time permits, I will explain how this is related to the dimension of alpha-beta sets, and describe recent examples that show that the problem is more delicate than anticipated.
13:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Prof. Dr. Alexander Polishchuk (Univ. of Oregon and FIM)
Equations of some birational models of M_g,n. abstract
Abstract:
I will discuss examples of birational models of M_{g,n} that on the one hand are given as GIT-quotients for torus actions on explicit affine schemes, and on the other hand admit modular descriptions. I’ll focus mostly oncases g=0 and g=1.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Ruben Mud (Independent)
Abstract:
The geometrically intuitive notion of betweenness was first formally introduced by Pasch in 1882. Since then, it has found applications in graph theory, combinatorics, artificial intelligence, and circuit design. In this talk, we will argue that enriched categories form a natural framework to reason about betweenness geometry. It turns out that there is a functorial correspondence between the category of betweenness spaces and the category of enriched categories. Using this correspondence, we obtain new interpretations of betweenness with potential applications to causal discovery.
Paolo Bonicatto (Università degli Studi di Trento)
Abstract:
It is well known that, given a Sobolev function vanishing in a measurable set, the gradient must vanish almost everywhere on that set. This property is usually called "locality of the gradient operator". In the seminar, we will introduce the notion of locality for general linear (first-order) differential operators and we will discuss some sufficient and necessary conditions for locality to hold. We will present several examples and, if time allows, a complete catalogue of differential operators in the 2D setting. This is part of ongoing projects with G. Alberti (Pisa) and G. Del Nin (MPI, Leipzig).
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
John Baldwin (Boston College)
Characterizing traces for knots abstract
Abstract:
There has been a lot of interest in understanding which knots are characterized by which Dehn surgeries. In this talk, I\'ll propose studying a 4-dimensional version of this question: which knots are determined by the orientation-preserving diffeomorphism types of which traces? I\'ll discuss several results that are in stark contrast with what is known about characterizing slopes; for example, that every algebraic knot is determined by its 0-trace. Moreover, every positive torus knot is determined by its n-trace for any n <= 0, whereas no non-positive integer is known to be a characterizing slope for any positive torus knot besides the right-handed trefoil. Our proofs use tools from Heegaard Floer homology and results about surface homeomorphisms.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Ana Djurdjevac (Freie Universität Berlin)
Quantitative approximation of the Dean-Kawasaki equation with interactions abstract
Abstract:
Interacting particle systems provide flexible and powerful models that are useful in many application areas such as sociology (agents), molecular dynamics (proteins) etc. However, particle systems with large numbers of particles are very complex and difficult to handle, both analytically and computationally. Therefore, a common strategy is to derive effective equations that describe the time evolution of the empirical particle density. A prototypical example that we will consider is the formal identification of a finite system of particles with the singular Dean-Kawasaki equation.Our aim is to introduce a well-behaved nonlinear SPDE that approximates the Dean-Kawasaki equation for a particle system with mean-field interaction both in the drift and the noise term. We want to study the well-posedness of these nonlinear SPDE models and to control the weak error of the SPDE approximation with respect to the particle system using the technique of transport equations on the space of probability measures.This is the joint work with H. Kremp, N. Perkowski and J. Xiaohao.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Susan R. Wolf (University of North Carolina)
19:30 • Universität Bern