Internal Seminar of CRM-CNRS

The CRM-CNRS is holding its internal seminar on Tuesday, February 18, 2025, in room 4336 (André Aisenstadt Pavilion, University of Montreal), from 9:30 AM to 1:00 PM.

Four scientific presentations will be given by:

• Sébastien Darse;
• Emmanuel Royer;
• Ewen Gallic;
• Thierry Daudé.

Program

9:30 AM: Sébastien Darses

Some themes around the zeta function.

We will talk a bit about analytic continuation and approximation problems. The presentation will be very accessible and does not require any particular knowledge beyond a bachelor’s degree.

10:15 AM: Emmanuel Royer

Exponential sums

I will present exponential sums, their relevance to number theory, and some approaches to tackle them.

11:00 AM – 11:30 AM: Break

11:30 AM: Ewen Gallic

Algorithmic fairness through counterfactual analysis and optimal transport.

This presentation will explore ways to address fairness issues in predictive modeling, echoing societal or legal requirements. It will begin by examining how different disciplines define discrimination and fairness, in order to prepare for a more targeted discussion on algorithmic fairness. Fairness will be defined more precisely in the context of the insurance industry, considering its impact on decision-making processes and focusing on predictive models producing risk scores. The presentation will then introduce methods to quantify the (in)fairness of predictive models. Finally, it will present a mitigation approach based on counterfactual analysis: assuming a causal structure represented by directed acyclic graphs (DAGs), a sequential method for constructing counterfactuals will be proposed, relying on optimal transport. The presentation will also address the often-overlooked case of categorical data, where data is represented in the simplex, and where a Dirichlet-type transport is applied to ensure fairness between protected and unprotected groups.

12:15 PM: Thierry Daudé

An introduction to the Calderón inverse problem.

The Calderón inverse problem consists of determining the physical properties inside a body (such as its electrical conductivity) from measurements made on the surface of that body. In mathematical terms, given a compact Riemannian manifold with boundary, one seeks to reconstruct the Riemannian metric from the knowledge of the associated Dirichlet-to-Neumann operator. In this talk, I will review some major advances in this problem and conclude with some counterexamples to uniqueness obtained with my collaborators Niky Kamran and François Nicoleau.

Welcomed on delegation by the CNRS for a long-term stay at CRM-CNRS, Sébastien Darses is a lecturer at Aix-Marseille University.

A professor at Université Clermont-Auvergne, Emmanuel Royer is on delegation for institutional functions by the CNRS, to lead the CRM-CNRS.

Welcomed on delegation by the CNRS for a long-term stay at CRM-CNRS, Thierry Daudé is a lecturer at Aix-Marseille University, Aix-Marseille School of Economics.

Welcomed on delegation by the CNRS for a long-term stay at CRM-CNRS, Ewen Gallic is a lecturer at Université Marie et Louis Pasteur.