Seminar on periods and motives | Feynman periods as Apéry limits

Time：2023-12-21, Thursday, 16:00-17:00

Venue：Zoom Meeting ID: 276 366 7254 Passcode: YMSC

Organizer：Jin Cao (THU), Ma Luo (ECNU)

Speaker：Erik Panzer University of Oxford

Abstract：

To prove that zeta(3) is irrational, Apéry realized this number as the limit of the ratio of two solutions of a linear recurrence with polynomial coefficients. Similar recurrences and their "Apéry limits" have been studied in mirror symmetry. In this talk, I will sketch a method to realize Feynman integrals as Apéry limits, using a combinatorial graph invariant from arXiv:2304.05299. Examples include fourth order recurrences for zeta(3,5) and a third order recurrence for zeta(5) and zeta(9). The mechanism behind this method is a general theory (applicable beyond Feynman integrals) based on a Mellin transform, and furthermore connecting "diagonal" coefficients of powers of a polynomial (combinatorics) with point-counts over finite fields (arithmetic). This is work in progress together with Francis Brown.

About the Speaker:

Erik Panzer

University of Oxford

Research interests

Feynman graphs and Feynman integrals, hyperlogarithms, (elliptic) polylogarithms, (elliptic) multiple zeta values, motivic periods, combinatorial Hopf algebras, renormalization, resummation

Personal website

https://people.maths.ox.ac.uk/panzer/

DATEDecember 21, 2023

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