Time: 16:30-18:00

Location: Mondi 3

Speaker 1: Mischa Elkner (Hausel group)

Title: Harmonics in Lie Theory

Abstract: Several mathematical developments of the 20th century were inspired by the spherical harmonics, which give rise to an orthonormal basis for the L2 space of the sphere. From an algebraic point of view, this comes from a decomposition of arbitrary polynomials into radial and harmonic polynomials. At the source of these facts is the standard action of the (Euclidean) rotation group. After reviewing these ideas, I will present how Kostant applied them to understand another group action -- that of a Lie group on its Lie algebra -- and sketch how this connects to my research.

Speaker 2:  Ondrej Draganov (Edelsbrunner group)

Title: Topological Data Analysis and Mathematical Experiments

Abstract: I have two goals for my MIX talk — to give you an idea what topological data analysis (TDA) is about, and to convince you that computational experiments are a meaningful tool in theoretical mathematics. I will first introduce persistent homology, one of the main tools in TDA, and describe its variant for colored point sets that I worked on during my PhD. Then I will tell a story about how coding and running random examples led us to interesting questions in discrete geometry.