Schedule
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Monday, July 10, 2023 ›
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09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
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›11:30 (1h30)
Greta Panova - Asymptotic Algebraic Combinatorics, Part 1
Algebraic Combinatorics studies objects and quantities originating in Representation Theory and Algebra via combinatorial tools. It has seen many connections with Probability and Statistical Mechanics both in terms of the objects (e.g. plane partitions are dimer covers of a region in the hexagonal grid) and tools (symmetric functions, R matrices, cluster algebras etc). I will cover the necessary background (Young tableaux, Schur functions etc) and some of the corresponding techniques to study dimers. I will then introduce some of the outstanding problems in Algebraic Combinatorics concerning (asymptotic) analysis of structure constants, show some approaches via Probability and Statistical Mechanics and present further open problems which may inspire application and development of other such tools.
› Amphi 15
›14:30 (45min)
Tomas Berggren - Geometry of the doubly periodic Aztec dimer model
We will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit we see three types of macroscopic regions -- known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of the rough region, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.
› Amphi 15
›15:15 (45min)
Christophe Garban - Surface law and charge rigidity for the Coulomb gas on ℤ^d
I will start by introducing and motivating the (two-component) Coulomb gas on the d-dimensional lattice ℤ^d. I will then present some puzzling properties of the fluctuations of this Coulomb gas. The connection of this model with integer-valued fields and compact-valued spin systems will be emphasised through the talk. This is based on joint works with Avelio Sepúlveda and David Dereudre.
› Amphi 15
›16:30 (45min)
Alessandra Occelli - Universality of multi-component stochastic systems
Universality classes are identified by exponents and scaling functions that characterise the macroscopic behaviour of the fluctuations of the thermodynamical quantities of interest in a microscopic system. When considering multi-component systems different universality classes might appear according to the asymmetry of the interactions. To see which universality classes might appear, we outline the approach of Nonlinear Fluctuation Hydrodynamics Theory (NLFHT), introduced by Spohn 2014. As an example, we study the equilibrium fluctuations of an exclusion process evolving on the discrete ring with three species of particles named A,B and C. We prove that proper choices of density fluctuation fields (that match of those from nonlinear fluctuating hydrodynamics theory) associated to the conserved quantities converge, in the large N limit, to a system of stochastic partial differential equations, that can either be the Ornstein-Uhlenbeck equation or the Stochastic Bur
› Amphi 15
›18:00 (4h)
› Zamansky Tower, 24th floor
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Amphi 15
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