The graduate student seminar meets from 2:00 to 3:20 pm Thursdays in Goldsmith 226. Want to give a talk? Email Steve Hermes at srhermes@etc... for details.
The question of how to hold a fair election has plagued thinkers since the Enlightenment. In the last century, this question has been subjected to mathematical rigor; in his 1950 Ph.D. thesis, however, Kenneth Arrow gave a startlingly straightforward proof that, in some sense, no fair election procedure can exist. In this talk, I'll work through some historical proposals for voting methods, motivate and prove Arrow's theorem, and, if time permits, explore some ideas for how to pick up the pieces.
Mirror symmetry first made the leap from the world of theoretical physics into mathematics in 1991 when Candellas, de la Ossa, Green, and Parkes used the phenomenon to calculate the number of rational curves of a given degree on a generic quintic. To this day the mirror symmetry is mysterious from the eyes of Mathematics. In his 1994 ICM address, Maxim Kontsevich proposed a category theoretic interpretation of mirror symmetry called the Homologcial Mirror Symmetry Conjecture. In this talk I will attempt to explain the conjecture and develop the ingredients necessary for its formulation. The material should be accessible to everyone willing to take some of the rudiments of manifolds and differential forms on faith.