Difference between revisions of "Algebraic Geometry Seminar Spring 2015"

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(Fall 2014 Schedule)
(Jose Rodriguez)
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== Abstracts ==
 
== Abstracts ==
 +
 +
===Jordan Ellenberg===
 +
Furstenberg sets and Furstenberg schemes over finite fields
 +
 +
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===
 
===Jose Rodriguez===
 
TBA
 
TBA

Revision as of 20:31, 15 January 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

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