Algebraic Geometry Seminar Spring 2015

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Revision as of 11:43, 28 January 2015 by Maxim (talk | contribs) (Fall 2014 Schedule)
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The seminar meets on Fridays at 2:25 pm in Van Vleck B135.

The schedule for the previous semester is here.

Algebraic Geometry Mailing List

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Fall 2014 Schedule

date speaker title host(s)
January 30 Manuel Gonzalez Villa (Wisconsin) Motivic infinite cyclic covers
February 20 Jordan Ellenberg (Wisconsin) Furstenberg sets and Furstenberg schemes over finite fields I invited myself
February 27 Botong Wang (Notre Dame) TBD Max
March 6 Matt Satriano (Johns Hopkins) TBD Max
March 13 Jose Rodriguez (Notre Dame) TBD Daniel
March 27 Joerg Schuermann (Muenster) TBD Max


Manuel Gonzalez Villa

Motivic infinite cyclic covers (joint work with Anatoly Libgober and Laurentiu Maxim)

We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) an element in the Grothendieck ring, which we call motivic infinite cyclic cover, and show its birational invariance. Our construction provides a unifying approach for the Denef-Loeser motivic Milnor fibre of a complex hypersurface singularity germ, and the motivic Milnor fiber of a rational function, respectively.

Jordan Ellenberg

Furstenberg sets and Furstenberg schemes over finite fields (joint work with Daniel Erman)

We prove a theorem of Kakeya type for the intersection of subsets of n-space over a finite field with k-planes. Let S be a subset of F_q^n with the "k-plane Furstenberg property": for every k-plane V, there is a k-plane W parallel to V which intersects S in at least q^c points. We prove that such a set has size at least a constant multiple of q^{cn/k}. The novelty is the method; we prove that the theorem holds, not only for subsets of the plane, but arbitrary 0-dimensional subschemes, and reduce the problem by Grobner methods to a simpler one about G_m-invariant subschemes supported at a point. The talk will not assume that everyone in the room is an algebraic geometer.

Jose Rodriguez