Algebraic Geometry Seminar Spring 2015

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

• Please join the Algebraic Geometry Mailing list to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).

Fall 2014 Schedule

date	speaker	title	host(s)
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

Abstracts

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

TBA