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Dynamics of random interfaces and tilings of the plane

Date: Monday, March 4, 2019 10:00 - 11:00
Speaker: Fabio Toninelli (CNRS Lyon)
Location: Mondi Seminar Room 2, Central Building
Series: Mathematics and CS Seminar
Host: Laszlo Erdös


I will start from the following apparently simple question, motivated by non-equilibrium statistical physics. Given an integer L, color the points "x" of Z^d black for |x|How does the set of black sites evolve macroscopically, as L and the time tend to infinity?
I will show that this question is actually quite challenging and it is related to several interesting mathematical objects: (i) to anisotropic curve shortening flows in the d=2 case, (ii) to random tilings of the plane in the d=3 case; and (iii) to the computation of the running time of probabilistic Markov Chain Monte Carlo sampling algorithms on complex combinatorial structures.
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