Topic: **A quantitative central limit theorem for the simple symmetric exclusion process**

Abstract. *We will discuss a quantitative central limit theorem for the simple symmetric exclusion process on a multidimensional discrete torus. Our argument is based on a comparison of the generators of the density fluctuation field of the symmetric exclusion process and the generalized Ornstein-Uhlenbeck process, as well as on an infinite-dimensional Berry-Essen bound for the initial particle fluctuations. The obtained rate of convergence is optimal. It is a joint work with Benjamin Gess.*

Topic: **Phase Diagrams of Lattice Models with Competing Interactions**

Abstract. *The existence of competing interactions lies at the heart of a variety of original phenomena in magnetic systems, ranging from the spin-glass transitions found in many disordered materials to the modulated phases with an infinite number of commensurate regions, that are observed in certain models with periodic interactions. Ising models with competing interactions has recently been considered extensively because of the appearance of nontrivial magnetic orderings. If competing interactions are defined on prolonged second or third nearest-neighbors, i.e. spins belonging to the same branch then corresponding phase diagram is very rich, and if second or third nearest-neighbors belong to different branches of the tree then corresponding phase diagram consists of paramagnetic, ferromagnetic, paramodulated with period p = 2 and anti-ferromagnetic phases. It is shown that for 1-D Ising model with competing interactions one can reach phase transition while for usual 1-D Ising model we don’t reach phase transition.*

Topic: **Hitting times in random graphs**

Abstract. *I will discuss a general approach to derive nearly-exact formulas for average hitting times in large graphs. As a main example, we will consider the case of the stochastic block model with two communities, though the idea is much more general. Time permitting, I will explain the connection with community detection.*

Topic: **Filtration problem for SDE with interaction**

Topic: **Dynamics of random knots, quantum physics and compacts in Hilbert space**

Topic: **Chen-Strichartz formula for SDE with interaction**

Topic: **On point densities for Arratia flows with drift**

Topic: **On Reflected Diffusions in Cones and Cylinders**

Topic: **Control problem for SDE with interaction**

Topic: **On clusters in coalescing stochastic flows**