Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in english. If not, they will be marked as **Spanish Only.**

## Dynamics of unipotent frame flows on hyperbolic manifolds

ABSTRACT: Joint work with B. Schapira. After explaining the geometry of the objects, we give another proof of a theorem of A. Mohammadi and H. Oh about the ergodicity of the Burger-Roblin measure for Kleinian groups of high enough critical exponents and relate it with a topological counterpart.

## Absence of eigenvalues of Schrödinger, Dirac and Pauli Hamiltonians via the method of multipliers.

Abstract: Originally arisen to understand characterizing properties connected with dispersive phenomena, in the last decades the method of multipliers has been recognized as a useful tool in Spectral Theory, in particular in connection with proof of absence of point spectrum for both self-adjoint and non self-adjoint operators. In this seminar we will see the developments of the method reviewing some recent results concerning self-adjoint and non self-adjoint Schrödinger operators in different settings, specifically both when the...

## Non-bijective scaling limit of maps via restrictions.

Abstract: In recent years, scaling limits of random planar maps have been the subject of a lot of attention. So far, the convergence of these random combinatorial objects relies heavily on bijections. In this talk, I will present a non-bijective technique that allows to obtain the convergence of a random map model, using a convergent closely related random map model. Then, I will present a new result which is obtained using our technique: the Brownian disk is the limit of quadrangulations with a simple boundary, when the boundary is of order...

## Quantum Mean Field Asymptotics and Multiscale Analysis

Abstract: In a joint work with Z. Ammari, and F. Nier, we study how multiscale analysis and quantum mean field asymptotics can be brought together. In particular we study when a sequence of one-particle density matrices has a limit with two components: one classical and one quantum. The introduction of “separating quantization for a family” provides a simple criterion to check when those two types of limit are well separated. We also give examples of explicit computations of such limits, and how to check that the separating...

## Fredholm groupoids

Resume : In many cases, the study of linear partial differential equations on a singular manifold can be related to that of a Lie groupoid whose action generates the (pseudo)differential operators of interest. Obtaining Fredholm conditions for these operators leads to the definition of Fredholm groupoids as recently introduced by Carvalho, Nistor and Qiao and also studied by Côme. I will introduce theses objects and give examples to illustrate the notion of Fredholm groupoids.

## Le Jugement Majoritaire, une nouvelle théorie du choix social

Abstract: Le Jugement Majoritaireest une nouvelle théorie du choix social applicable à toute prise de décision collective, établie par les chercheurs du CNRS Michel Balinski et Rida Laraki à partir de 2006. En adoptant une toute nouvelle perspective du vote pour tenter de répondre au théorème d’impossibilité d’Arrow, elle résout les paradoxes de l’élection constatés par Condorcet et Arrow. L’électeur vote en évaluant individuellement tous les candidats, à partir d’une échelle commune et ordinale du mentions (par...

## The median rule in judgement aggregation (joint work with Klaus Nehring).

Abstract: I will first briefly introduce social choice theory in general. I will then move onto the subfield of judgement aggregation, and discuss some recent research on this topic. In a judgement aggregation problem, we begin with a set K of logically interconnected propositions, called issues. A view is an assignment of a truth-value to each issue in K. However, not all views are admissible; some may violate the logical relationships between the different issues in K. Suppose that each individual voter has a logically consistent view; we...

## On the unreasonable effectiveness of the Sinkhorn algorithm

Abstract: This talk concerns Sinkhorn algorithm, broadly understood as the iterative scaling of a matrix that realizes the solution of an entropy regularized linear program subjected to row and column constraints. I will present new theoretical and applied results that demonstrate the effectiveness of this procedure in two contexts: first, Sinkhorn algorithm implements the solution of an entropy regularized version of optimal transport. I will show this regularization substantially improves sample complexity over the unregularized case, a...

## Latent distance estimation for random geometric graphs.

Abstract: Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent positions of nodes of the network. The connection probabilities between the nodes are determined by an unknown function (referred to as the “link” function) evaluated at the distance between the latent points. We introduce a spectral estimator of the pairwise distance between latent...

## An Introduction to Reinforcement Learning and Reward Machines.

In Reinforcement Learning (RL), an agent is guided by the rewards it receives from the reward function. Unfortunately, it may take many interactions with the environment to learn from sparse rewards, and it can be challenging to specify reward functions that reflect complex reward-worthy behavior. We propose using reward machines (RMs), which are automata-based representations that expose reward function structure, as a normal form representation for reward functions. We show how specifications of reward in various formal languages, including...