Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

28.04.2026

Raum 1.013, Rudower Chaussee 25

Daniel Huybrechts (Universität Bonn)

Title: TBA

Abstract: 

30.06.2026

Raum 1.013, Rudower Chaussee 25

Pascal Hubert (Aix-Marseille Université)

Title: Complexity of Polygonal Billiards

Abstract: Given a polygon in the plane, one can code a billiard trajectory by the sequence of sides its intersects. The complexity is the number of  words of a given length we get this way starting from any point with any initial direction.  It is a measure of the disorder of the dynamical system. Katok considered this problem as one of the most resistant one in dynamics. For rational polygons, following results of Howard Masur, one can get cubic lower and upper bounds. I will explain recent results obtained with Athreya and Troubetzkoy. For regular polygons, we get a cubic asymptotic behavior for this quantity. With Athreya, Forni and Matheus, we find an error term for this counting. 

11.11.2025

Erwin-Schrödinger-Zentrum, Rudower Chaussee 26, Raum 0'101 (Erdgeschoss, gegenüber Gerdans Cafe)

Stephen Wright (Computer Sciences Department, University of Wisconsin-Madison)

Title: Optimization in Theory and Practice

Abstract: Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their theoretical properties, optimization algorithms are interesting also for their practical usefulness as computational tools for solving real-word problems. There are often gaps between the practical performance of an algorithm and what can be proved about it. These two facets of the field — the theoretical and the practical — interact in fascinating ways, each driving innovation in the other. This work focuses on the development of algorithms in two areas — linear programming and unconstrained minimization of smooth functions — outlining major algorithm classes in each area along with their theoretical properties and practical performance, and highlighting how advances in theory and practice have influenced each other in these areas. In discussing theory, we focus mainly on non-asymptotic complexity, which are upper bounds on the amount of computation required by a given algorithm to find an approximate solution of problems in a given class.