Time: 16:30-18:00

Location: Mondi 3 / Central Building

Speaker 1: Viacheslav Goncharov (first year student)

Title: Algebra and geometry of octonions

Abstract: There are four normed division algebras over the real numbers: R, C, H and O. While the first three are widely known, the last one — the octonions, which are not even associative — is much less famous. We will discuss their construction and their relation to the exceptional Lie algebras via geometry. The topic is classical, and the goal of the talk is to share a beautiful piece of mathematics with the audience.

Speaker 2:  Lenka Kopfová (Kwan group)

Title: Moran process under strong selection

Abstract: The Moran process is a model used in evolutionary game theory to study natural selection. In this process, a population of individuals, represented by a graph, evolves in steps. In one step, a random individual is selected with probability proportional to its fitness and spreads to its randomly selected neighbor. The classical course of study is to consider an individual with a hereditary mutation and examine the fate of this mutation in time. We study a modified version of the Moran process that corresponds to the strong selection, as in the dynamics of invasive species. In this process, only the mutant individuals spread and eventually conquer the whole population. The key quantity that we study is the so-called fixation time, which is the expected time until all individuals become mutants. We give tight upper and lower bounds for fixation time on a general population structure and refine them for some classes.