## Jerry Yu Fu : A density theorem towards p-adic monodromy

- Number Theory ( 450 Views )We investigate the $p$-adic monodromy of certain kinds of abelian varieties in $\mathcal{A}_{g}$ and prove a formal density theorem for the locus of deformations with big monodromy. Also, we prove that the small monodromy locus of the deformation space of a supersingular elliptic curve is $p$-adic nowhere dense. The approach is based on a congruence condition of $p$-divisible groups and transform of data between the Rapoport-Zink spaces and deformation spaces.

## Chad Schoen : A family of surfaces constructed from genus 2 curves

- Algebraic Geometry ( 197 Views )This talk is about complex analytic geometry, the field of mathematics concerned with complex manifolds and more generally with complex analytic spaces. The "curves" of the title are compact Riemann surfaces and the "surfaces" in the title are compact complex manifolds of dimension 2 over the complex numbers (and hence dimension 4 over the real numbers). The talk will explore the problem of constructing two dimensional complex manifolds by deforming known complex analytic spaces. It will focus on a single example. The talk should be quasi-accessible to anyone who has courses in Riemann surfaces and algebraic topology.

## David Herzog : Hypocoercivity for Langevin dynamics

- Probability ( 167 Views )This will be the last in his sequence of an introductory lecture on Hypocoercivity for Langevin dynamics. For those who have not attended the previous lectures and are familiar with Langevin dynamics, the talk should be accessible. We will continue our discussion on convergence to equilibrium for second-order Langevin dynamics using the Poincare approach. We'll recap convergence in H^1(\mu) and then we'll talk about the direct L^2(\mu) method of Dolbeault, Mouhot, and Schmeiser, also called the DMS approach.

## Joe Jackson : The convergence problem in mean field control

- Probability ( 121 Views )This talk will be about the convergence problem in mean field control (MFC), i.e. the challenge of rigorously justifying the convergence of certain "symmetric" $N$-particle stochastic control problems towards their mean field counterparts. On the one hand, this convergence problem is already well-understood from a qualitative perspective, thanks to powerful probabilistic techniques based on compactness. On the other hand, quantitative results (i.e. rates of convergence) are more difficult to obtain, in large part because the value function of the mean field problem (which is also the solution to a certain Hamilton-Jacobi equation on the Wasserstein space) may fail to be $C^1$, even if all the data is smooth. After giving an overview of the convergence problem, I will discuss the results of two recent joint works with Cardaliaguet, Daudin, Delarue, and Souganidis, in which we use some ideas from the theory of viscosity solutions to overcome this lack of regularity and obtain rates of convergence of the $N$-particle value functions towards the value function of the corresponding MFC problem.

## Eylem Zeliha Yildiz : Braids in planar open books and fillable surgeries.

- Geometry and Topology ( 97 Views )We'll give a useful description of braids in $\underset{n}{\#}(S^1\times S^2)$ using surgery diagrams, which will allow us to address families of knots in lens spaces that admit fillable positive contact surgery. We also demonstrate that smooth $16$ surgery to the knot $P(-2,3,7)$ bounds a rational ball, which admits a Stein handlebody. This answers a question left open by Thomas Mark and Bülent Tosun.