Harmonic Mappings with Free Boundaries and their Heat Flows (Lecture 5) by Yannick Sire скачать в хорошем качестве

Harmonic Mappings with Free Boundaries and their Heat Flows (Lecture 5) by Yannick Sire

Program: Geometric Analysis and PDE ORGANIZERS: Ali Hyder (TIFR-CAM, Bangalore, India), Sandeep K (TIFR-CAM, Bangalore, India), Debabrata Karmakar (TIFR-CAM, Bangalore, India) and Yannick Sire (Johns Hopkins university, Baltimore, USA) DATE & TIME: 02 February 2026 to 13 February 2026 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru Geometric analysis has emerged as one of the most dynamic research areas over the past several decades. This field captivates scholars by exploring geometric problems through the lens of analytical tools and differential equations, showcasing an intriguing interplay between these disciplines. The subject encompasses a wide spectrum of topics, each requiring a unique approach, as there is no single unifying theory to resolve all challenges. The partial differential equations (PDEs) arising in these fields are notably diverse. For example, questions related to conformal geometry pertain to elliptic equations. Likewise, the Ricci flow, pivotal to the resolution of the renowned Poincaré conjecture, is classified as a nonlinear parabolic PDE. Additionally, various equations stemming from the general theory of relativity exhibit hyperbolic characteristics. These distinctions highlight that the mathematical tools necessary for addressing different problems vary greatly. In this workshop, we aim to delve deeply into several key themes lying within the fascinating realm of nonlinear elliptic and parabolic equations and the calculus of variations. We will cover essential topics such as conformal geometry, harmonic maps, isoperimetric problems, the Ginzburg-Landau system, and mass transport problems. We welcome everyone to join us in this workshop and deepen our understanding of these fascinating subjects. CONTACT US: gpde@icts.res.in PROGRAM LINK: https://icts.res.in/program/gpde