Prof. Nalini Anantharaman (Universität Straßburg)
Title: From Quantum Chaos to Random Surfaces
Abstract: A hundred years ago, Einstein wondered about quantization conditions for classically ergodic systems. However, a mathematical description of the spectrum of Schrödinger operators associated to ergodic classical dynamics is still missing today. The main paradigm where these questions are studied in mathematics concerns the spectrum of the Laplacian on a hyperbolic manifold. I will review the three main conjectures in quantum chaos, asking to show universal behaviour for eigenvalues and eigenfunctions of these operators.
The explosion of recent results on the universality of the spectrum of random graphs gives the hope that introducing randomness may help to make progress understanding the issues of quantum chaos. I will, in particular, introduce models of random hyperbolic surfaces, discuss Mirzakhani's work and a few recent results concerning the spectrum of the Laplacian of random hyperbolic manifolds.
Kulturvortrag von Professor Jun Mitani (Universität Tsukuba)
Title: The Art and Science of Curved Origami
Abstract: While origami is an art form original to the Japanese culture that creates geometric shapes from a single sheet of paper, origami has attracted the mathematics community and is part of thriving ongoing research. The basic operation of origami folding typically involves straight folds that enclose flat areas. However, paper can be flexibly bent to form curved surfaces, known as developable surfaces. The talk will touch the mathematics of curved foldings and their outreach to engineering applications, to movies (Shin Godzilla) and trophy designs (Rugby).
