Mathematics Colloquium

Thursday, November 2, 2017
4:20 PM - 5:20 PM (ET)
Exley Science Center Tower ESC 121
Event Type
Canalia, Caryn

Jonathan Huang, Wes

Title: Zeta Functions, Witt rings, and a Classical Formula of MacDonald

Abstract:A remarkable formula of MacDonald provides a closed expression for the generating series of the Poincaré polynomial of the symmetric powers Symn X of a space X. We show that this formula takes a very nice form when rewritten in the big ring of Witt vectors W ([z]) of the polynomial ring [z]. We then provide some motivation for similarly viewing the Hasse-Weil zeta function of varieties over finite fields as elements in the big Witt ring W (). In this setting, the zeta function Z(X, t) takes the form of an Euler-Poincaré characteristic.

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