We consider several classes of sequences of random variables whose Laplace transform presents the same type of \textit{splitting phenomenon} when suitably rescaled. Answering a question of Kowalski-Nikeghbali, we explain the apparition of a universal term, the \textit{Gamma factor}, by a common feature of each model, the existence of an auxiliary randomisation that reveals an independence structure.
The class of examples that belong to this framework includes random uniform permutations, random polynomials or random matrices with values in a finite field and the classical Sathe-Selberg theorems in probabilistic number theory. We moreover speculate on potential similarities in the Gaussian setting of the celebrated Keating and Snaith's moments conjecture. (Joint work with R. Chhaibi)
 

Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite dimensional spaces. We show that the convergence rate for
the Poisson approximation of the Brownian motion is as expected proportional to λ −1/2 where λ is the intensity of the Poisson process. We also exhibit the speed of convergence for the Donsker Theorem and extend this result to enhanced Brownian motion.

 

We will discuss a result to the effect that the moduli space of log stable maps to a toric variety X is "the same" as the Morse-theoretic moduli space of broken gradient flow lines in the "differentiable realization" Y of the fan for X.  This is joint work with Sam Molcho.

Smooth cubic fourfolds are linked to K3 surfaces via their Hodge structures, due to work of Hassett, and via Kuznetsov's K3 category A. The relation between these two viewpoints has recently been elucidated by Addington and Thomas. 
We study both of these aspects further and extend them to twisted K3 surfaces, which in particular allows us to determine the group of autoequivalences of A for the general cubic fourfold. Furthermore, we prove finiteness results for cubics with equivalent K3 categories and study periods of cubics in terms of generalized K3 surfaces.

Who are you?  What motivates you?  What's important to you?  How do you react to challenges and adversities?  In this session we will explore the power of self-awareness (understanding our own characters, values and motivations) and introduce assertiveness skills in the context of building positive and productive relationships (with colleagues, collaborators, students and others).

Computing distinct solutions of differential equations -- Patrick Farrell

Abstract: TBA

Triangles and equations -- Yufei Zhao

Abstract: I will explain how tools in graph theory can be useful for understanding certain problems in additive combinatorics, in particular the existence of arithmetic progressions in sets of integers. 

Writing is a part of any career in science or mathematics. I will make some remarks about the role writing has played in my life and the role it might play in yours.