Feynman Graphs, Periods and Polylogarithms

Seminar schedule, abstracts and guide to the literature 

Unless otherwise announced, the seminar meets on Wednesdays 2:15pm at CM 105.

November 14th

Benjamin Doyon (Durham) Vertex operator algebras and zeta values 

A natural way of interpreting the sum of all natural numbers is to set it equal to zeta(-1)=-1/12. Zeta values at negative integers also occur when one "simplifies" the central term of the bracket relations of the central extension of certain Lie algebras of formal differential operators, thus providing nice modular properties to their graded character. Oddly enough, these two occurences of zeta values are connected. I will explain how this happens, using the Heisenberg Lie algebra and the general theory of vertex operator algebras, to which I will try to give a good introduction.

November 21st

Govind Krishnaswami (Durham) Shuffle products in Yang-Mills theory and matrix models

We discuss certain algebraic and differential structures of the factorized Schwinger-Dyson equations of large-N matrix models and Yang-Mills theory.
The appearance of shuffle and concatenation products and their derivations is explained. The shuffle product is naturally viewed as the pointwise
product of functions on Loop(M), written in terms of tensors on the manifold M. We will try not to assume any prior knowledge of Yang-Mills theory,
matrix models or shuffle products.

 

November 28th

Govind Krishnaswami (Durham) Shuffle products in Yang-Mills theory and matrix models

Part 2

 

December 12th

special "Feynman Graphs and Periods Day" instead of the seminar

December 19th

Abhijnan Rej (Bonn and Durham) TBA