Thursday, 3rd November 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

Professor Yakov Varshavsky

(Hebrew University)

"Lefschetz trace formula and Deligne's conjecture"

** Abstract: **
Let *f* be a continuous map from a "nice" compact
topological space *X* to itself. Then *f* induces an
endomorphism *H^i(f)* of the cohomology groups *H^i(X,Q)* of
*X* for each *i*, and the classical Lefschetz trace formula
asserts that the virtual trace *\sum_i (-1)^i Tr(H^i(f))*
can be described in terms of the fixed points of *f*.

This result has various applications. For example, it gives a one line proof of the famous Brouwer's fixed point theorem.

In the 60's Grothendieck et al. showed that analogs of the Lefschetz trace formula also hold in algebraic geometry. As a consequence, he proved famous Weil conjectures on the number of points of algebraic varieties over finite fields, which is currently one of the most important results in the area.

In my lecture I will describe these results, give some of their applications and discuss recent developments.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2005-06

Archive of talks