Tutte Colloquium - Karen Yeats

Friday, November 24, 2023 3:30 pm - 3:30 pm EST (GMT -05:00)

Title: Diagonal coefficients, graph invariants with the symmetries of Feynman integrals, and the proof of the c_2 completion conjecture

Speaker: Karen Yeats
Affiliation: University of Waterloo
Location: MC 5501

Abstract: In a scalar field theory the contribution of a Feynman diagram to the beta function of the theory, the Feynman period, can be written as an integral in terms of the (dual) Kirchhoff polynomial of the graph. There are many interesting graph theoretic operations under which this integral is invariant, and we can better understand the period and its geometry by investigating graph invariants with these same symmetries. Recently Erik Panzer found a new such invariant coming from a particular coefficient of the Martin polynomial.  Together we used this to prove an over 10 year old conjecture on an arithmetic graph invariant known as the c_2 invariant, and came to understand that diagonal coefficients of Kirchhoff polynomials tie together many of the known graph invariants with the symmetries of Feynman periods and unlock previously inaccessible proofs.

Joint work with Erik Panzer