Schedule
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Tuesday, July 11, 2023 ›
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09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
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›9:30 (1h30)
Greta Panova - Asymptotic Algebraic Combinatorics, Part 2
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
›11:30 (1h30)
Ioan Manolescu - Exploring the critical phase of 2D FK-percolation, Part 1
In these lectures we will study FK-percolation (also called the random-cluster model) on the square lattice Z^2. Our focus will be on recent results describing the phase transition, namely: its sharpness; its continuity/discontinuity depending on the cluster parameter q; the large-scale rotational invariance of the critical models. These results have been obtained through a wide variety of techniques; of particular interest will be the relationship between FK-percolation and the six-vertex model, and the treatment of the latter using the transfer matrix formalism.
› Amphi 15
›14:30 (45min)
Kalle Kytölä - Local fields of lattice models and conformal field theories
A fundamental feature any conformal field theory (CFT) is a representation of Virasoro algebra on the space of local fields of the theory: Virasoro algebra describes the effect of (infinitesimal) conformal transformations on the fields. By combining discrete holomorphicity and Sugawara-type constructions, we showed that also the spaces of suitably defined lattice local fields of the Ising model and the discrete Gaussian free field (DGFF) have Virasoro representations. Similarly, a Virasoro representation for local fields of the double-dimer model has been recently found by Adame-Carrillo. Having a Virasoro representation on the local fields of these lattice models opens up the possibility of a direct correspondence, preserving the Virasoro actions, between lattice model local fields and CFT local fields. We will discuss such a 1-to-1 correspondence for local fields of the DGFF and a Fock space of local fields of a free boson CFT (which is generated under operator product expansions [..
› Amphi 15
›15:15 (45min)
Mirjana Vuletic - Free boundary Schur process
Free boundary Schur process is a generalization of the original Schur process of Okounkov and Reshetikhin, with no restrictions on boundary partitions. This model after "shift-mixing" is a Pfaffian process. This talk will be about models and asymptotic results related to this process. The limiting behavior for these models is given by some new deformations of universal distributions of Schur processes. The talk is based on a joint work with D. Betea, J. Bouttier, and P. Nejjar.
› Amphi 15
›16:30 (45min)
Alexander Glazman - Delocalisation of height functions
We will discuss the delocalisation of height functions in two dimensions. The main example will be the six-vertex model when a,b \leq c \leq a+b. Our approach applies also to integer-valued Lipschitz functions (loop O(2) model): we show delocalisation when 1/2 \leq x^2 \leq 1. The main idea behind the argument is a novel FKG property for a joint distribution of spin and percolation configurations. It enables the use of the non-coexistence theorem of Zhang and Sheffield. If time permits, we will also discuss how to derive from this a new proof for the continuity of the phase transition in the random-cluster model. In the delocalised regime, the height functions are expected to converge to the Gaussian free field. This is so far known only at the line a^2 + b^2 = c^2 (dimer model) and in its neighbourhood. Based on a joint work with Piet Lammers.
› Amphi 15
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Amphi 15
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