Numerical Methods, Uncertainty Quantification, and Optimal Transport Theory - CEMRACS 2022

Explore advanced mathematical concepts through this comprehensive lecture series from the 2022 CEMRACS summer school. Delve into numerical methods and uncertainty quantification for kinetic equations with Giacomo Dimarco, learning computational approaches for solving complex mathematical models that describe particle behavior and transport phenomena. Master trajectory inference techniques using Schrödinger bridges through Lénaïc Chizat's three-part series, discovering how to reconstruct optimal paths between probability distributions with applications in machine learning and data analysis. Examine integro-differential models of evolutionary adaptation in changing environments with Sepideh Mirrahimi, understanding how mathematical frameworks can model biological evolution and population dynamics. Build foundational knowledge in optimal transport theory with Filippo Santambrogio, exploring the mathematical framework for efficiently moving mass distributions and its applications across various fields including economics, machine learning, and image processing.