Woensdag 9 mei 2007
Spreker: 
Abhijnan Rej (MPI Bonn)

Titel: 
Hypersurfaces from Feynman graphs

Tijd: 
11:00  12:00

Plaats: 
HG00.307

Vanaf kwart voor 11 is er koffie en thee in de
binnenstraat
(voor de zaal).
Abstract
Given a Feynman graph, one obtains a singular hypersurface in a
projective space of dimension equal to the number of edges of the graph
by setting the Kirchhoff polynomial of that graph to zero. These
hypersurfaces have a very rich geometry and recently
BlochEsnaultKreimer have studied motives (in the sense of
Grothendieck) attached to hypersurfaces for a certain class of Feynman
graphs. This leads to a surprising connection between arithmetic
algebraic geometry and quantum field theory.
In the first part of my talk, I will survey the general properties of
graph hypersurfaces and the emerging motivic theory of Feynman graphs
and integrals. In the second part of my talk, I will describe my ongoing
work with C. Bergbauer on the geometry and topology of hypersurfaces of
Feynman graphs that are obtained by inserting one Feynman graph into
another.