ENYGMMa V

Schedule 

11:30 am - 1:00 pm Lunch in the Cantor Lounge 

1:10 pm  - 2:00 pm Talk by Evita Nestoridi

2:00 pm  - 2:20 pm Break

2:20 pm  - 3:10 pm Talk by Lucy Yang

3:10 pm - 4:00 pm Tea

Titles and Abstracts

Evita Nestoridi: Leading all the way

Xander and Yola run a ''random race'' as follows.  A continuous probability distribution $\mu$ on the real line is chosen.  The runners begin at zero.  At time $i$, Xander draws $\X_i$ from $\mu$ and advances that distance, while Yola advances by an independent drawing $\Y_i$.  After $n$ such moves, Xander wins a valuable prize provided he not only wins the race but leads after every step; that is, $\sum_{i=1}^k \X_i > \sum_{i=1}^k \Y_i$ for all $k = 1,2, \dots, n$.  What distribution is best for Xander, and what then is his probability of getting the prize? The answers to these questions are joint work with Peter Francis and Pete Winkler.

Lucy Yang: The algebra of vector bundles

Vector bundles are families of vector spaces parametrized by another topological space. The collection of vector bundles on a space X gives rise to an algebraic invariant called the Grothendieck group K^0(X) of X which generalizes the dimension of vector spaces. We will see how Grothendieck groups and the additional algebraic structure they carry may be used to put restrictions on the existence of certain sums of squares formulas. We consider why a paradigm shift from "property" to "structure" gives rise to higher K-groups. Time permitting, we discuss bundles with additional structure (e.g. algebraic, symmetric bilinear forms) and computational tools for higher K-groups.