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Speaker: Grigory Solomadin, RUDN University

Topic: «Lexicographical shelling of matroids; simplicial polytopes and g-theorem»

Abstract: In the next lecture we will introduce a particularly useful construction for shelling of matroids. In what follows, we advance to the study of combinatorics of polytopes. We will prove the Dehn-Sommerville relations on h-numbers of convex polytopes in Euclidean space by applying shellability concept. We will start to discuss the g-theorem, which describes the values of the f-vector on simplicial polytopes.