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Full Description
This volume includes expanded lecture notes from the Mathemata Summer School and Festum Pi 2024 conference, held in Chania, Crete, in July 2024. The lectures focus on advanced analysis techniques for tackling problems in mathematical physics, covering recent advancements in the study of phase transitions, interacting particle systems, kinetic theory, qualitative properties of degenerate Vlasov equations, optimal transport methods for parabolic diffusion equations, and Ricci flow. This volume serves as a valuable resource for researchers exploring modern developments in mathematical analysis. Additionally, it includes two lectures on music theory, reflecting the spirit of Festum Pi 2024.
Contents
Foreword (Dionysios Dervis-Bournias).-- Introduction (Nicholas Alikakos & Cédric Villani).- Part I: Modelling and derivation.-1. Graph and Mean-Field Limits for Interacting Particles Systems (Nathalie Ayi).-2. Four Lectures on The Mathematical Theory of (multi) Phase Transitions (Nicholas Alikakos).- Part II: Analysis Tools.- 3. Introduction to Quantitative De Giorgi Methods (Giovanni Brigati & Clément Mouhot).- 4. Optimal transport methods for parabolic diffusion equations: the JKO scheme (Filippo Santambrogio).- 5. Resonances and computations (Yvan Bruned, Frédéric Rousset & Katharina Schratz).- Part III: Advances in specific programs.- 6. Splitting maps in Type I Ricci flows (Panagiotis Gianniotis).- 7. Fisher Information in Kinetic Theory (Cédric Villani).- Part IV: Music and mathematics, a gentle bridge.- 8. Microtones, 31-Tet and Just Intonation (Franck Jedrzejewski).- 9. From bird feather to digits: Some thoughts about Olivier Messiaen (Claude Ledoux).



