Theory Seminar

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.
Slides