Speaker: Professor Emanuel Indrei （Kennesaw State University）

Time: July, 24/26/27, 15:00-16:00

Place: Room 312, Mathematics Bulding 

Title: The Almgren problem 

Abstract: The Almgren problem appears in classical thermodynamics when one seeks to understand whether minimizing the free energy with a potential g ≥0, g(0) = 0 in the class of sets of finite perimeter under a mass constraint generates a convex minimizer representing a crystal assuming solely that the sub-level sets {g < t} are convex. Historically, this is one of the most complex problems to analyze and one of the most important problems in physics. The physical principle connecting minimizers to crystals was independently discovered by Gibbs in 1878 and Curie in 1885. Only a handful of convexity results exist for all masses, even in two dimensions. In the lectures, we will investigate the minimization problem. More specifically, we will investigate the existence and convexity in one and two dimensions and also the state-of-the-art in higher dimension.