Speaker: Sergey Galkin

Title: Inequalities and their extremes

Date: Dec 5, 2011, 16:15 - 17:45

Place: Seminar Algebraische Geometrie, Freie Universitaet, Berlin

I'll demonstrate a few interrelated (some famous and some new) incarnations of the following meta-mathematical principle: objects that saturate a natural inequality have distinguished discrete, arithmetic and combinatorial nature. First example is Mason-Stothers inequality and Belyi functions. Second example is Szpiro(-Beauville-Miranda-Persson-Shioda-Tate) inequality and extremal elliptic surfaces. Third example is a natural linearization-generalization of the second one: Golyshev's inequality and extremal local systems. If time permits I'll show some other incarnations or explain why mirror reflections of Fano varieties is a generalizations of the inequality of arithmetic and geometric means.