**UBC Mathematics Department**

*http://www.math.ubc.ca*

## Colloquium Abstract: Dr. Gordon Slade, McMaster Univ.

*Polymers, Percolation, and Critical Exponents *

Abstract: Linear polymer molecules are modelled by self-avoiding
walks and branched polymers are modelled by lattice trees and lattice
animals. It is widely believed that the number and typical size of
self-avoiding walks and of lattice trees and animals are governed by
dimension-dependent universal critical exponents. Similar critical
exponents arise in percolation theory, an elementary model of a phase
transition of interest in probability theory and statistical
mechanics. This lecture, intended for a general mathematical
audience, describes joint work with Takashi Hara proving existence of
critical exponents for these models in high dimensions, using a method
known as the lace expansion.

*Coffee, tea and cookies will be served in Math Lounge (Annex) Room 1115

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