Graduate Lectures in Mathematics (6/12)

26 October 2022

Sebastian Baader

Prof. Claire Burrin (Universität Zürich) & Prof. Anders Karlsson (Université de Genève)

The purpose of these traditional lectures is to present recent important developments in mathematics to a large audience of graduate students and young researchers. The lecturers are chosen as experts in their field, with demonstrated pedagogical talent.

Wednesdays, 13h15-14-45: Prof. Anders Karlsson

Metric geometry and its applications

This will be a course on metric spaces and their most natural morphisms: maps that preserve or do not increase distances. Basic notions such as geodesics, Busemann functions, the metric compactification, nonpositive curvature, Gromov hyperbolicity, fixed point theorems, classifications of isometries will be explained in detail. In parallel we will study several concrete and important metric spaces. One leitmotif will be the analogy with functional analysis, and how the metric theory completes the linear theory as it were. Another will be the great variety of mathematical and scientific topics where metrics nowadays arise. The latter will be illustrated along the way, by showing how the metric notions and results discussed find application in group theory, operator theory, dynamical systems and differential equations, complex analysis, topology, deep learning and stochastic games.

Wednesdays, 15h00-16h30: Prof. Claire Burrin

Title: Spectral theory of hyperbolic surfaces

Abstract: The Laplacian plays a prominent role in many parts of mathematics. On a flat surface like the torus, its spectrum is the subject of Fourier analysis, whose 19th century development allowed to solve the heat and wave equations. On the sphere, one is led to study spherical harmonics. In this course, we will discuss hyperbolic surfaces, study their spectrum, and explore some applications to geometry and number theory.

University of Bern, Room B78, building ExWi, Sidlerstrasse 5, 3012 Bern

math.cuso.ch/activities/internal-program

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