Monday, January 12, 2009
Freie Universität Berlin
Institut für Informatik
Lecture - 14:15
What if you play your favorite two-player game, such as Hex or Chess, but
instead of alternating moves you bid each time for the right to move? The
basic mathematical theory of such games is simple and elegant, with a
surprising relation to random-turn games, in which the right to move is
determined by a coin flip. In this talk, I will survey the twenty-year
history of bidding games, with special emphasis on the subtleties of
discrete versus real-valued bidding, and discuss how recent results of Oded
Schramm and his collaborators lead to powerful probabilistic artificial
intelligence engines for Bidding Hex.
Colloquium - 16:00
The Ehrhart $\delta$-vector of a lattice polytope $P$ encodes the number of lattice points in all dilates of $P$. It is a long standing unsolved problem to determine which vectors can be realised as Ehrhart $\delta$-vectors of some lattice polytope. In this direction, we establish a new series of inequalities between the coefficients of the Ehrhart $\delta$-vector of a lattice polytope containing an interior lattice point.