Schedule

The miniconference will consist of talks and open problem session.

  • 9:00-9:30 Karen Yeats, Overview of the miniconference
  • 9:40-10:30 Erik Panzer, The Hepp bound for Feynman periods
  • 10:30 -10:50 coffee break
  • 10:50 - 11:20 Michael Borinsky, Counting graphs without given edge-induced subgraphs
  • 11:30 -12:00 Alejandro Morales, The Legendre and Fourier transforms for formal power series
  • 12:00 - 1:50 lunch
  • 1:50 - 2:20 Matilde Marcolli, Feynman quadrics-motive of the massive sunset graph
  • 2:30 - 3:00 Iain Crump, The coproduct as a linear combination of factorizable graphs
  • 3:00 -3:30 coffee break
  • 3:30-4:30 - joint with the Tutte Colloquium - Freddy Cachazo, Combinatorics in Particle Interactions
  • 4:30 - 5:00 open problem session (please bring problems!)


Titles and abstracts (click links in titles for slides)

Inspired from renormalization in QFT, we can define a Hopf algebraic structure on graphs which allows us to construct generating functions of graphs, which do not contain edge-induced subgraphs from a given set. I will present this algebraic structure and, as an example, use it to relate the generating function of all graphs with the generating function of bridgeless graphs. Both generating functions are related by a Legendre transformation.


  • Freddy Cachazo (Perimeter) Combinatorics in Particle Interactions (*Tutte Colloquium)

The main approach for testing physical theories of particles is via scattering experiments. The traditional approach for computing theoretical predictions uses Feynman diagrams.


  • Iain Crump (Waterloo) The coproduct as a linear combination of factorizable graphs

We show that every 4-point phi-4 graph with at most logarithmic subdivergences has a reduced coproduct that can alternately be written as a linear combination of factorizable graphs.


We prove that the Feynman quadrics-motive of the massive sunset graph is generically not mixed-Tate. Moreover, we describe the motive explicitly in terms of a Prym variety. Based on joint work with Goncalo Tabuada.


In perturbative quantum field theory, the partition function and the effective action are fundamental objects though with analytic obstacles when considered as functionals since they generally do not converge. We consider these in the zero dimensional case as well-defined formal power series with the physical information encoded in the coefficients. We show that the fundamental Legendre and Fourier transforms between these generating functions can be defined unambiguously as well-defined maps between the coefficients of these formal power series. Joint work with Achim Kempf and David M. Jackson.


  • Erik Panzer (Oxford) The Hepp bound for Feynman periods

The Hepp bound is a rational number associated to Feynman graphs that respects the known symmetries of the corresponding integrals. I will illustrate a graph theoretical and a geometric interpretation of the Hepp bound and discuss some of its interesting properties.


  • Karen Yeats (Waterloo) Overview of the miniconference

I will point out in very broad strokes some different ways we see combinatorial structures in perturbative quantum field theory, and how, as best I understand it, the work of the other conference participants connects to this central theme.