At the interface of physics and combinatorics
Organizer and Chair: Karen Yeats
(Simon Fraser University, Canada)
- JULIEN COURTIEL, Simon Fraser University
Enumeration of planar maps with additional structures [PDF]
Initiated by Tutte in the sixties in order to prove the four color theorem, the enumeration of planar maps has appeared to be interesting in statistical physics, where the maps constitute a discrete model for surfaces. Since the enumeration of bare planar maps is well understood nowadays, the attention has focussed on maps equipped with an additional structure: spanning trees, Ising/Potts models, percolation...
After a quick introduction on the Potts model, we will show several recent enumerative results about planar maps equipped with a spanning forest. Finally, we will mention as a prospect the problem of percolation on planar maps.
- ERIK PANZER, Institute des Hautes Etudes Scientifiques
Linearly reducible Feynman graphs [PDF]
Feynman integrals describe scattering processes of elementary particles and are associated to a graph. An important subset of these integrals, called linearly reducible, can be expressed in terms of multiple polylogarithms. Such functions may be represented by words and we sketch the combinatorial algorithm which can be used to compute them. Then we address the interesting open question of how to characterize and recognize the class of linearly reducible Feynman graphs. The goal is to describe these combinatorially, and we will present recent new results.
- STU WHITTINGTON, University of Toronto
Self-avoiding walks and polymer adsorption [PDF]
Self-avoiding walks interacting with a confining line or plane are a standard
model of polymer adsorption. When a force is applied an adsorbed polymer can
be desorbed and the self-avoiding walk model can be modified to include
the effect of a force. This talk will largely focus on rigorous results about
the model that give information about the form of the phase diagram (the
temperature dependence of the critical desorption force) and the order of the phase
transition, though some numerical results will also be discussed. This is mainly joint
work with Buks van Rensburg, Tony Guttmann and Ivan Jensen.
- KAREN YEATS, Simon Fraser University
The renormalization group equation viewed combinatorially [PDF]
The renormalization group equation is an extremely important differential equation in quantum field theory. If we think of the perturbative expansion as an augmented generating function what does the renormalization group equation say? I will explain two related answers to this question.