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Presented By: Department of Mathematics

MCAIM Colloquium Seminar

Planar Ising model: convergence results on regular grids and s-embeddings of irregular graphs into R^{2,1}

In the first part of the talk we briefly discuss convergence results obtained during the last fifteen years for the critical Ising model on the square lattice. This research program was started by Smirnov in the mid-2000s and is based on the discrete holomorphicity of fermionic observables. Smirnov's ideas were later developed by a number of authors including the speaker, similar results were also obtained for the near-critical model and for the Z-invariant model on rhombic lattices. However, until very recently it was unclear what a generalization of these techniques for irregular graphs should look like. In the second part of the talk we discuss a new tool: the so-called s-embeddings of planar graphs carrying the Ising model into the Minkowski space R^{2,1}. These embeddings can be thought of as a certain analogue of classical Tutte's harmonic embeddings and, among other things, naturally lead to an appearance of quasi-conformal mappings in the planar Ising model context.

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Meeting ID: 914 9404 8285
Passcode: 387662
Speaker(s): Dmitry Chelkak (École Normale Supérieure, Paris)

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