Calendar

We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. Higgs-Coulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wall-crossing results for GLSM and generalizes Landau-Ginzburg/Calabi-Yau correspondence. The talk is based on a joint work in progress with Melissa Liu.

https://harvard.zoom.us/j/97335783449?pwd=S3U0eVdyODFEdzNaRXVEUTF3R3NwZz09

In the study of Ising models on large locally tree-like graphs, in both rigorous and non-rigorous methods one is often led to understanding the so-called belief propagation distributional recursions and its fixed point (also known as Bethe fixed point, cavity equation etc). In this work we prove there is at most one non-trivial fixed point for Ising models with zero and certain random external fields.

As a concrete example, consider a sample A of Ising model on a rooted tree (regular, Galton-Watson, etc). Let B be a noisy version of A obtained by independently perturbing each spin as follows: Bv equals to Av with some small probability δ and otherwise taken to be a uniform +-1 (alternatively, 0). We show that the distribution of the root spin Aρ conditioned on values Bv of all vertices v at a large distance from the root is independent of δ and coincides with δ=0. Previously this was only known for sufficiently low-temperature” models. Our proof consists of constructing a metric under which the BP operator is a contraction (albeit non-multiplicative). I hope to convince you our proof is technically rather simple.

This simultaneously closes the following 5 conjectures in the literature: uselessness of global information for a labeled 2-community stochastic block model, or 2-SBM (Kanade-Mossel-Schramm’2014); optimality of local algorithms for 2-SBM under noisy side information (Mossel-Xu’2015); independence of robust reconstruction accuracy to leaf noise in broadcasting on trees (Mossel-Neeman-Sly’2016); boundary irrelevance in BOT (Abbe-Cornacchia-Gu-P.’2021); characterization of entropy of community labels given the graph in 2-SBM (ibid).

Joint work with Qian Yu (Princeton).

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class S[A1]. I will describe the resulting geometric structures using a kind of complexified Hitchin system parameterising bundles on curves equipped with pencils of flat connections.

Zoom Link: https://cuhk.zoom.us/j/94410733353

Meeting ID: 944 1073 3353
Passcode: 20220223

For details, please visit:

http://www.ims.cuhk.edu.hk/cgi-bin/SeminarAdmin/bin/Web

http://www.ims.cuhk.edu.hk/activities/seminar/joint-dg-seminar/

In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields:  Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity.  The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime).  In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

https://harvard.zoom.us/j/977347126
Password: cmsa

In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.

This is based on joint works with Ovidiu Savin from Columbia University.

Zoom ID: 950 2372 5230 (Password: cmsa)

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological

disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes:

1. (i) to explain the tortoise & hare story in bacterial competition: how motility of Pseudomonas aeruginosa bacteria leads to a slower invasion of bacteria colonies, which are individually faster, and
2. (ii) how self-propelled defects lead to finding an unanticipated mechanism for cell death.

I will then discuss various strategies to tame, otherwise chaotic, active flows, showing how hydrodynamic screening of active flows can act as a robust way of controlling and guiding active particles into dynamically ordered coherent structures. I will also explain how combining hydrodynamics with topological constraints can lead to further control of exotic morphologies of active shells.

Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

https://harvard.zoom.us/j/977347126
Password: cmsa