Jun Nonaka (Waseda)
A sequence of π/3-equiangular hyperbolic polyhedra abstract
Abstract:
A polyhedron is called π/k-equiangular if all its dihedral angles are equalto π/k ( k ∈ N ). In this talk, we will first introduce some known resultsabout such polyhedra in hyperbolic spaces. Then, we will construct asequence of π/3-equiangular three-dimensional hyperbolic polyhedra dif-ferent from the sequence Atkinson found in 2009. We will also determinethe volumes of some of these polyhedra
10:20 • Université de Fribourg, room Phys 2.52
Prof. Dr. Sébastien Biebler (Université Paris Cité)
Non-density of hyperbolicity in complex dynamics in several variables abstract
Abstract:
One of the main goals in the theory of dynamical systems is to describe the dynamics of a "typical" map. For instance, in the case of diffeomorphisms of a given manifold, it was conjectured by Smale in the 60s that uniform hyperbolicity was generically satisfied. This hope was however fast discouraged by exhibiting dynamical systems displaying in a robust way dynamical configurations which are obstructions to hyperbolicity: robust homoclinic tangencies (this is the so-called Newhouse phenomenon) and robust heterodimensional cycles. In this talk, I will explain these phenomena and their extensions to the complex setting. In particular, I will show how to construct robust heterodimensional cycles in the family of polynomial automorphisms of C^3. The main tool is the notion of blender coming from real dynamics.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Danilo Lewanski (University of Trieste)
A fair amount of weighted intersection numbers summing up to zero abstract
Abstract:
Via virtual localisation techniques, Johnson, Pandharipande and Tseng proved that the integral of the Hodge class over the moduli space of admissible covers vanishes under certain sufficient technical conditions: either strong negativity or negativity together with boundedness would suffice. What happens when these conditions are lifted? The answer (in a certain setting) was provided in previous work with Borot, Do, Karev and Moskovsky: the vanishing of a single summand gets replaced by the vanishing of the sum of many. This was achieved as a byproduct of the topological recursion procedure. By deformation techniques in topological recursion, other three families of these relations arose, two of which genus dependent.Based on joint work with Gaëtan Borot and Maksim Karev, tested thanks to the admcycles Sage package.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Marius Tiba
Erdos covering systems abstract
Abstract:
Since their introduction by Erdos in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding the existence of covering systems with various properties. In 1950, Erdos asked if there exist covering systems with distinct arbitrary large moduli. In 1965, Erdos and Selfridge asked if there exist covering systems with distinct odd moduli. In 1967, Schinzel conjectured that in any covering system there exists a pair of moduli, one of which divides the other. In 2015, Hough resolved Erdos\' problem showing that a finite collection of arithmetic progressions with distinct sufficiently large moduli does not cover the integers. We established a quantitative version of Hough\'s theorem estimating the density of the uncovered set, thus answering a question posed by Filaseta, Ford, Konyagin, Pomerance and Yu from 2007. Additionally, we resolved the Erdos-Selfridge problem in the square free case as well as Schinzel\'s conjecture in full generality. In this talk, we discuss these results and present a gentle exposition of the methods used. This talk is based on joint work with Paul Balister, Bela Bollobas, Rob Morris and Julian Sahasrabudhe.
14:15 • EPF Lausanne, CM 1 517
Anuj Kumar (UC Berkeley)
Abstract:
We construct nonunique solutions of the transport equation in the class $L^\\infty$ in time and $L^r$ in space for divergence free Sobolev vector fields $W^{1, p}$. We achieve this by introducing two novel ideas: (1) In the construction, we interweave the scaled copies of the vector field itself. (2) Asynchronous translation of cubes, which makes the construction heterogeneous in space. These new ideas allow us to prove nonuniqueness in the range of exponents beyond what is available using the method of convex integration and sharply matchwith the range of uniqueness of solutions from Bruè, Colombo, De Lellis \'21.
14:15 • Universität Basel, Online via Zoom
Isacco Nonino (University of Glasgow)
Smooth structures on non-compact 4-manifolds abstract
Abstract:
When studying smooth structures on a 4-dimensional topological manifold M, there are three main topics one has to cover: existence, uniqueness and behavior of their diffeotopy groups.I will explain the reasons why the 4 dimensional case is so interesting and wild, and remark the striking difference between the compact and non-compact settings.I will then give an overview on the recent work on diffeotopy groups of exotic smoothings of R4, and show how the results were generalized to a wider class of non-compact 4 manifolds.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Vincent Perrier (Inria, France)
How to preserve a divergence or a curl constraint in a hyperbolic system with the discontinuous Galerkin method abstract
Abstract:
Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the vorticity for the first order wave system or divergence preservation for the Maxwell system or the induction equation. In this talk, I will address this problem with the classical discontinuous Galerkin method. Based on discrete de-Rham ideas, I will show that by considering an adapted approximation space (but still discontinuous) for vectors , divergence or curl can be easily preserved under mild assumption on the numerical flux
16:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 1.2
Weijun Xu (Beijing)
Periodic homogenisation for 2D gPAM abstract
Abstract:
We consider periodic homogenisation problem for two dimensional generalised parabolic Anderson model, a model problem of a singular SPDE beyond Da Prato - Debussche trick. The goal is to understand how the two singular limiting procedures, homogenisation and renormalisation, interact with each other. One key ingredient is to identify a suitable ansatz uniform in the homogenisation parameter in a nontrivial SPDE setting. Based on a joint work with Yilin Chen (PKU) and Ben Fehrman (LSU).
16:00 • EPF Lausanne, Bernoulli Center
Prof. Dr. Vincent Vargas (Universität Genf)
CANCELLED: Harmonic analysis of Gaussian multiplicative chaos on the circle abstract
Abstract:
Gaussian multiplicative chaos (GMC) on the circle is a canonical (random) multifractal measure on the circle which appears in a wide variety of contexts and most recently in relation to Liouville conformal field theory. In this talk, I will present the first results concerning the decay and renormalization of the Fourier coefficients of GMC. In particular, one can show that GMC is a so-called Rajchman measure which means that its Fourier coefficients go to zero when the frequency goes to infinity. Numerous questions remain open. Based on a joint work with C. Garban.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43