Time: 16:30-18:00 (TBC)

Location: Mondi 3

Speaker 1 (ISTA): Oleksii Kolupaiev (Erdös Group)

Title: Flow of fractional free convolution powers

Abstract: Free convolution of measures is an operation within the framework of free probability theory, analogous to the classical convolution of measures. Without delving deeply into free probability, we can define free convolution using the language of random matrix theory. By considering the free convolution of a measure with itself multiple times, we arrive at the concept of a sequence of free convolution powers of a given measure. Interestingly, this sequence can be extended to a flow, which is generally impossible in the classical setting. We will explore the properties of this flow and discuss several related open questions.

Speaker 2 (Vienna):  Yannic Wentzel (Schertzer Group, UniVie)

Title: Why a football pitch can be a good approximation of a large species' habitat

Abstract: How does the structure of a habitat influence the relatedness of the populations living there? Intuitively, it makes sense that the heterogeneous environmental conditions of the Brazilian rainforest should lead to very different genetic architectures than the homogeneous environmental conditions of a football pitch. Using a stochastic model and techniques from mixing time theory, we explain why the genetic diversity within large species living on a football pitch can actually be a good approximation for the genetic diversity of a large species living in a heterogeneous environment.