Spring 2024
Monday 4.15 - 5.15 pm
Room 2-147
Scheduled virtual talks will be held on Zoom, Monday 4:15-5:15 pm.
Zoom Link
Schedule
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February 5
Matan Harel
(Northeastern University)The loop O(n) model and the XOR trick
Abstract: The loop O(n) model is a model for random configurations of non-overlapping loops on the hexagonal lattice, which contains many models of interest (such as the Ising model, self-avoiding walks, and random Lipshitz functions) as special cases. Its conjectured phase diagram is very rich, and the model is believed to undergo several different phase transitions. Over the last decade, several features of the phase diagram have been proven rigorously, mostly through the use of particular bijections or observables at critical values. We use an expansion around critical percolation to prove that, near the values that correspond to critical Bernoulli percolation, the loop O(n) model has long , infinitely-nested loops, without relying on exact solvability. This is joint work with Nick Crawford, Alexander Glazman, and Ron Peled.
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February 12
Kevin Yang
Scaling limits for random growth driven by reflecting Brownian motion
Abstract: We discuss long-time asymptotics for a continuum version of origin-excited random walk. It is a growing submanifold in Euclidean space that is pushed outward from within by the boundary trace of a reflecting Brownian motion. We show that the leading-order behavior of the submanifold process is described by a flow-type PDE whose blow-ups correspond to changes in diffeomorphism class of the growth process. We then show that if we simultaneously smooth the submanifold as it grows, fluctuations of an associated height function are described by a regularized KPZ equation with noise modulated by a Dirichlet-to-Neumann operator. If the dimension of the manifold is 2, we show well-posedness of the singular limit of this regularized KPZ-type equation. Based on joint work with Amir Dembo.
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February 19
Presidents Day
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February 26
Tomas Berggren
(MIT)Geometry of the doubly periodic Aztec dimer model
Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, 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 these regions, 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.
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March 11
Jiaming Xu
(Duke)Recent advances on random graph matching
Abstract: Random graph matching aims to recover the hidden vertex correspondence between two random graphs from correlated edge connections. This is a ubiquitous problem arising in a variety of applications across diverse fields such as network privacy, computational biology, computer vision, and natural language processing. The problem is also deep and rich in theory, involving the delicate interplay of algorithms, complexity, and information limits. Recently, extensive efforts have been devoted to the study of matching two correlated Erdős–Rényi graphs and exciting progress have been made, thanks to collective efforts from a wide research community. The speaker in his talk will present an overview, recent results, and important future directions on this topic. Based on joint work with Cheng Mao (Georgia Tech), Yihong Wu (Yale), and Sophie H. Yu (Stanford).
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March 18
Sky Cao
(MIT)Random surfaces and lattice Yang-Mills
Abstract: I will talk about recent work which studies Wilson loop expectations in lattice Yang-Mills models. In particular, I will give a representation of these expectations as sums over embedded maps. Time permitting, I will also discuss alternate derivations, interpretations, and generalizations of several recent theorems about Brownian motion limits (Dahlqvist), lattice string trajectories (Chatterjee and Jafarov) and surface sums (Magee and Puder).
This is joint work with Minjae Park and Scott Sheffield.
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March 25
Spring Break
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April 1
Guillaume Baverez
(Humboldt University of Berlin)Quantisation of the Segal's semigroup from Liouville theory
Abstract: In Segal's definition of conformal field theory (CFT), one key ingredient is to construct a representation of the semigroup of complex annuli with parametrised boundaries. In the first part of the talk, I will explain how this statement can be understood as a generalisation of the Hille-Yosida theorem, using only an analytic language. In particular, the (infinite dimensional) family of generators form a representation of the Virasoro algebra and encode the conformal symmetry of the theory. In the second part, I will give an example of this construction using the Gaussian free field, and show how it can be extended to treat the Liouville CFT. Based on joint works with Guillarmou, Kupiainen, Rhodes, Vargas.
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April 8
Shalin Parekh
(University of Maryland) -
April 15
Patriots' Day
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April 22
Pierre Patie
(Cornell) -
April 29
Jinwoo Sung
(University of Chicago) -
May 6
Brice Huang
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May 13