Felix-Klein-Kolloquium: Feynman 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.

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

Zeit: 17:15 - 18:30 Uhr

Ort: Gebäude 48, Raum 210

Die Vorträge des Felix-Klein-Kolloquiums finden jeweils um 17.15 Uhr im Raum 210 des Mathematik-Gebäudes 48 statt. Zuvor gibt es ab 16.45 Uhr die Gelegenheit, die Sprecherin oder den Sprecher beim Kolloquiumstee in Raum 580 zu treffen.