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Commutative Algebra and Algebraic Geometry April 15, 2014 (03:45 PM PDT - 06:00 PM PDT)
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Location: UC Berkeley, 939 Evans Hall
Speaker(s) I. Martin Isaacs (University of Wisconsin-Madison), François Loeser (Université de Paris VI (Pierre et Marie Curie))
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3:45 I. Martin Isaacs: Orbit sizes and an analog of the Alperin weight conjecture.

Let G be a finite group acting on a finite vector space V. Then G also acts on the dual space of V, and by general principles, the numbers of orbits in these two actions are equal. Although the sizes of the orbits in these actions generally do not agree, there are, nevertheless, some subtle relationships among these orbit sizes. The proof of the relevant theorem is not hard, but it involves a formula that is formally identical to the still unproved Alperin weight conjecture, which will be explained.


5:00 Francois Loeser: Monodromy and the Lefschetz fixed point formula

In 2002, in joint work with Jan Denef, we gave a formula expressing the Lefschetz numbers of iterates of the monodromy in terms of arc spaces  using direct computation on a resolution. In this talk we shall present a different proof, relying on a Lefschetz fixed point formula and non-archimedean geometry. This is joint work with Ehud Hrushovski.

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