Felix Klein Colloquium: Feyman periods - on graphs, integrals, polytopes and tropical physics

Seven decades ago, Feynman revolutionised perturbative calculations in particle physics. His recipe assigns an integral to each graph, and the sum of those integrals over all graphs describes a scattering process. This method is still an indispensable tool for computations that are needed to interpret measurements at experiments like the LHC at CERN.

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 explain 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.

Speaker: Dr. Erik Panzer, All Souls College, Oxford (UK)

Time: 17:15 - 18:30 o'clock

Place: Building 48, room 210

The lectures of the Felix Klein Colloquium will be held at 17:15 in room 210 of the Mathematics Building 48. Beforehand - from 16:45 - there will be an opportunity to meet the speaker at the colloquium tea in room 580.