Karoly Böröczky (Alfréd Rényi Institute of Mathematics)
The Isoperimetric inequality, the Brunn-Minkowski theory, and the Lp Minkowski problem
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Tsviqa Lakrec (Universität Zürich)
Equidistribution of affine random walks on tori and nilmanifolds abstract
Abstract:
I will discuss a quantitative equidistribution result for the random walk on a torus arising from the action of the group of affine transformations, and a generalization of these results to some nilmanifolds. This is a joint work with Weikun He and Elon Lindenstrauss.
Under the assumption that the Zariski closure of the group generated by the linear part acts strongly irreducibly on R^d we give quantitative estimates (depending only on the linear part of the random walk) for how fast this random walk equidistributes, unless the initial point and the translation part of the affine transformations can be perturbed so that the random walk is trapped in a finite orbit of small cardinality. In particular, this shows that the random walk equidistributes in law to the Haar measure if and only if the random walk is not trapped in a finite orbit. Under a certain condition, we can generalize this theorem to affine and linear random walks on a nilmanifold. This essentially extends the results of Bourgain-Furman-Lindenstrauss-Mozes and He-Saxcé for linear random walks on the torus.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Prof. Dr. Armin Schikorra (University of Pittsburgh)
Regularity results for n-Laplace systems with antisymmetric potential abstract
Abstract:
n-Laplace systems with antisymmetric potential are known to governgeometric equations such as n-harmonic maps between manifolds andgeneralized prescribed H-surface equations. Due to the nonlinearity ofthe leading order n-Laplace and the criticality of the equation theyare very difficult to treat.I will discuss some progress we obtained, combining stability methodsby Iwaniec and nonlinear potential theory for vectorial equations byKuusi-Mingione.Joint work with Dorian Martino
14:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
On high dimensional Dvoretzky–Kiefer–Wolfowitz type inequalities abstract
Abstract:
The DKW inequality is a non-asymptotic, high probability estimate on the L_\\infty distance between the distribution function of a real-valued random variable and its empirical (random) counterpart. Little was known on generalisations of that inequality to high dimensions, where instead of a single random variable one is interested in the behaviour of empirical distribution functions of a family of marginals of a random vector. Based on chaining methods, we show that the behaviour of various notions of distance (including the L_\\infty one) between the empirical and actual distributions of marginals in the given family can be fully characterised in terms of some (rather surprising) intrinsic complexity parameter of the family.Based on joint work with Shahar Mendelson.
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Stefan Czimek (Universität Leipzig)
Obstruction-free gluing for the Einstein equations abstract
Abstract:
We present a new approach to the gluing problem in General Relativity, that is, the problem of matching two solutions of the Einstein equations along a spacelike or characteristic (null) hypersurface. In contrast to previous constructions, the new perspective actively utilizes the nonlinearity of the constraint equations. As a result, we are able to remove the 10-dimensional spaces of obstructions to gluing present in the literature. As application, we show that any asymptotically flat spacelike initial data set can be glued to Schwarzschild initial data of sufficiently large mass. This is joint work with I. Rodnianski.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Loïs Faisant (Université Grenoble Alpes)
Motivic distribution of rational curves abstract
Abstract:
In diophantine geometry, the Batyrev-Manin-Peyre conjecture originally concerns rational points on Fano varieties. It describes the asymptotic behaviour of the number of rational points of bounded height, when the bound becomes arbitrary large.
A geometric analogue of this conjecture deals with the asymptotic behaviour of the moduli space of rational curves on a complex Fano variety, when the « degree » of the curves « goes to infinity ». Various examples support the claim that, after renormalisation in a relevant ring of motivic integration, the class of this moduli space may converge to a constant which has an interpretation as a motivic Euler product.
In this talk, we will state this motivic version of the Batyrev-Manin-Peyre conjecture and give some examples for which it is known to hold : projective space, more generally toric varieties, and equivariant compactifications of vector spaces. In a second part we will introduce the notion of equidistribution of curves and show that it opens a path to new types of results.
15:15 • EPF Lausanne, Salle MA A30
Nezhla Aghaee (University Odense & Université de Genève)
Combinatorial Quantisation of Super Chern Simons theory GL abstract
Abstract:
Chern-Simons theories with gauge supergroups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants In this talk we explain the combinatorial quantization of Chern- Simons theories and also the GL(1|1) generalization of it, for punctured Riemann surfaces of arbitrary genus. We construct the algebra of observables, and study their representations and applications to the construction of 3-manifold invariants. This work has also an application to Topological Phases of Matter.
16:15 • Université de Genève, Conseil Général 7-9, Room 1-07
Maryam Kamgarpour (EPF Lausanne)
Quantum CLearning equilibria in games with zeroth-order informationomputing for Numerical Simulation abstract
Abstract:
I address the question of learning equilibria in convex and non-convex games under zeroth-order information. In the convex setting, I will present our learning algorithm for monotone games that leverages estimation of game pseudo-gradient. I discuss extensions of the approach to a broader class of games as well as its convergence rates. In the non-convex setting, I will present our no-regret algorithm that leverages probabilistic estimation of a players\' cost function. I will compare the regret rate of the algorithm with the state-of-the-art and discuss our extensions to multi agent reinforcement learning.
16:15 • EPF Lausanne, Salle GA 3 21
Sylvia Serfaty (Courant Institute of Mathematical Sciences)
Systems of points with Coulomb interactions abstract
Abstract:
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the \'\'mean-field\'\' derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions,and finish with the description of the effect of temperature.
16:30 • UZH Zentrum, Building KO2, Room F 150