Feynman periods- on graphs, integrals, polytopes and tropical physics
by
Erik Panzer
→
Europe/Berlin
313 (MPI Meeting rooms)
313
MPI Meeting rooms
Description
A tremendous amount of research has been invested into the study of
Feynman integrals. Their theory is very rich and connects many
branches of mathematics in interesting ways. For example, recent
advances in the theory of motivic periods and their Galois theory have
led to new insights about Feynman integrals. However, we are far from
a complete understanding and the area remains very active and full of
open questions.
I will define a class of Feynman integrals to illustrate some of these
aspects, and discuss in particular the following problem:
When do two different graphs evaluate to the same integral?
In pursuing this problem, tools from combinatorics and algebraic
geometry have proven very fruitful. I will also sketch a new approach
inspired by tropical geometry, suggesting the study of a tropical
variant of the Feynman integral as an interesting invariant for graphs
and, more generally, matroids.
