Abstracts:

Searching for the Cup Product in Random Simplicial Complexes (Jonatan Kogan) 

The behavior of topological invariants of particular models of random simplicial complexes as the number of vertecies approaches infinity are an active area of study in recent years. In this lecture I introduce the lower-multi-parametric model, recall results about it by C.Fowler from 2019, and finally prove the triviality of the cup-product in a certain range in this model. A cursory knowledge of algebraic topology will be assumed.

Applications of homogeneous dynamics (Omri Solan) 

I will discuss homogeneous dynamics in view of two applications which inspired me: Rational Approximations of real vectors and Dirichlet's unit theorem.
If time permits we will see more applications.