Ted Chinburg will speak on connections between Gauss sums and arithmetic geometry. The best known connection of this kind is through the fact that the signs in the functional equations of L-series are products of Gauss sums. The Birch Swinnerton Dyer conjecture predicts that such signs determine the parity of the ranks of Mordell Weil groups. In some cases, work of Frohlich, Queyrut, Deligne and Saito shown various signs to be positive by identifying their local factors with Stieffel Whitney classes. I will talk about these results as well as a new method which proves the positivity of signs using hermitian Euler characteristics.