Another mathematical parable from the Book of Josh.

Calibration of Local Volatility Models with Stochastic Interest Rates using Optimal Transport
Joseph, B Loeper, G Obloj, J Finance and Stochastics
Random-Matrix Theory
Keating, J The Princeton Companion to Applied Mathematics 419-428 (01 Jan 2025)
Thu, 05 Jun 2025

11:00 - 12:00
C5

Relativistically invariant wave equations in the realist theory

Tristram de Piro
Abstract
Boris Zilber showed that you can build a logical structure around the relativistic Klein-Gordon and Dirac equations from quantum field theory. I will present the parallel realist theory, favoured by Einstein, to the Copenhagen interpretation. Starting from the requirements of Rutherford's principle for atomic systems and Maxwell's equations, I will show that there exist unique relativistically invariant wave equations for charge and current, with non-vacuum solutions. 
Thu, 15 May 2025

11:00 - 12:00
C5

A criterion for sharpness of the Elekes-Szabó theorem in positive characteristic

Lucas Nistor
(École Normale Supérieure )
Abstract

We establish that a criterion based on ring-theoretic amenability is both necessary and sufficient for the abelian version of the Elekes-Szabó theorem to be sharp in the case of positive characteristic. Moreover, the criterion is always sufficient. We provide illustrative examples in the theories ACF_p and DCF_0.

Congratulations to Renaud, elected as one of nine new Fellows for 2025 for "foundational contributions to network analysis and modeling, including community detection, the mathematics of random walks, and higher-order and multi-scale patterns in networks".

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