Seminar
| Parent Program: | -- |
|---|---|
| Location: | 50 Birge Hall, UC Berkeley |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
How many simple length $n$ trajectories one can draw on a lattice? It is easy to show that the number grows exponentially, but going beyond this observation is difficult. We will present our joint work with Hugo Duminil-Copin, giving a short and self-contained derivation of the Bernard Nienhuis conjecture that on hexagonal lattice this number grows like $(\sqrt{2+\sqrt{2}}^n$. Then we will discuss its relations to conformal invariance and other conjectured properties of the self-avoiding walk.
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