*Tid:* **5 september 2016 kl 15.15-16.15.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedtsvägen 25, plan 7.
Karta!
*Föredragshållare:*
**
Nathanael Berestycki (Cambridge)
**
**Titel:**
The dimer model: universality and conformal invariance.
**Abstract**
The dimer model on a finite bipartite planar graph is a uniformly chosen set of edges which cover every vertex exactly once. It is a classical model of statistical mechanics, going back to work of Kasteleyn and Temeperley/Fisher in the 1960s who computed its partition function.
I will discuss some recent joint work with Benoit Laslier and Gourab Ray, where we prove a general result which shows that when the mesh size tends to 0, the fluctuations are described by a universal and conformally invariant limit known as the Gaussian free field.
A key novelty in our approach is that the exact solvability of the model plays only a minor role. Instead, we rely on a connection to imaginary geometry, where Schramm--Loewner Evolution curves are viewed as flow lines of an underlying Gaussian free field. Hence the technique is quite robust and applies in a variety of situations.
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