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 Events
Cambridge
Fri 20 Oct 2017, 3:00pm
Department Colloquium
ESB 2012
Universality for the dimer model
ESB 2012
Fri 20 Oct 2017, 3:00pm-4:00pm

Abstract

The dimer model on a finite bipartite graph is a uniformly chosen perfect matching, i.e., a set of edges which cover every vertex exactly once. It is a classical model of mathematical physics, going back to work of Kasteleyn and Temeperley/Fisher in the 1960s, with connections to many topics including determinantal processes, random matrix theory, algebraic combinatorics, discrete complex analysis, etc.

A central object for the dimer model is a notion of height function introduced by Thurston, which turns the dimer model into a random discrete surface. I will discuss a series of recent results with Benoit Laslier (Paris) and Gourab Ray (Victoria) where we establish the convergence of the height function to a scaling limit in a variety of situations. This includes simply connected domains of the plane with arbitrary linear boundary conditions for the height, in which case the limit is the Gaussian free field, and Temperleyan graphs drawn on Riemann surfaces. In all these cases the scaling limit is universal (i.e., independent of the details of the graph) and conformally invariant.

A key new idea in our approach is to exploit "imaginary geometry" couplings between the Gaussian free field and Schramm's celebrated SLE curves.

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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UBC Math
Fri 3 Nov 2017, 3:00pm
Department Colloquium
ESB 2012
A Class of Polytopes with a Remarkable Volume Formula
ESB 2012
Fri 3 Nov 2017, 3:00pm-4:00pm

Abstract

TBA

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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Université Paris-Saclay
Wed 29 Nov 2017, 3:15pm SPECIAL
Department Colloquium
ESB 2012
TBA
ESB 2012
Wed 29 Nov 2017, 3:15pm-4:15am

Abstract


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Courant Institute, NYU
Fri 1 Dec 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA
ESB 2012
Fri 1 Dec 2017, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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Umberto Zannier
SNS, Pisa
Fri 2 Mar 2018, 3:00pm SPECIAL
Department Colloquium
ESB2012
PIMS-UBC Distinguished Colloquium--TBA
ESB2012
Fri 2 Mar 2018, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
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University of Oxford
Fri 6 Apr 2018, 3:00pm
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA
ESB 2012
Fri 6 Apr 2018, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.
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