Road to conquer the hardness - solving hard computational problems with generic tensor networks

BIMSA General Lecture

报告人 Jinguo Liu Harvard University and Hong Kong University of Science and Technology

时 间 2022-08-23 13:30-15:00 Tue

地 点 1120

Zoom 427 154 2002（PW: BIMSA）

组织者：程嵩

摘要

I will introduce a tensor network-based method to compute the solution space properties of a broad class of combinatorial optimization problems (e.g. spin glasses and hard core lattice gases). These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the hard core lattice gas as an example, I will demonstrate how the solution space properties can deepen our understanding, and help design better quantum algorithms.

Categorification of integral group rings extended by one dimension

BIMSA-Tsinghua Quantum Symmetry Seminar

报告人 Andrew Schopieray University of Alberta

时 间  2022-08-24 10:30-12:00 Wed

地 点 1110

Zoom 638 227 8222（PW: BIMSA）

组织者：刘正伟, Sebastien Palcoux, 王亦龙, 吴劲松

摘要

Fusion categories have established themselves in the past two decades as indispensable objects of study across representation theory, low-dimensional topological quantum field theory, conformal field theory, and quantum computation. But this field of study is at a cross-roads since the production of high-level machinery and abstraction is far out-pacing the set of known examples. At the core of this crisis is the "categorification" problem of determining when there exists a fusion category realizing a given fusion ring, i.e. the combinatorial skeleton of a fusion category. The most elementary fusion rings are the integral character rings of finite groups; it is still a vast open problem to determine which fusion rings with exactly one noninvertible element have corresponding fusion categories. In this talk we will discuss the categorification problem for fusion rings whose basis elements take one of two dimensions. This is the setting where almost all known "exotic" examples of fusion categories live. At least the first half of the talk will be understandable by a general audience. ([2208.07319] Categorification of integral group rings extended by one dimension (arxiv.org)).

3D gravity as an average large-c CFT

Geometry and Physics Seminar

报告人 Thomas Hartman Cornell University

时 间  2022-08-25 10:00-11:00 Thu

地 点 1129B

Zoom 638 227 8222（PW: BIMSA）

组织者：Hossein Yavartanoo

摘要

Euclidean wormholes have played an important role in recent progress on 2D gravity and on black hole information in higher dimensions. However, these spacetimes can also lead to puzzling results that seem to disagree with quantum mechanics and the AdS/CFT correspondence, which has led to the suggestion that wormholes arise from coarse-graining over UV degrees of freedom. I will explain the puzzle and show that Euclidean wormholes and other higher topology spacetimes in 3D gravity can be interpreted as averaged solutions of the 2D conformal bootstrap equations.

A two term Kuznecov sum formula

Seminar on microlocal analysis and applications

报告人 Yakun Xi Zhejiang University

时 间  2022-08-26 10:00-11:00 Fri

地 点

Zoom 618 038 6257（PW: SCMS）

组织者：金龙, 陈曦

摘要

A period integral is the average of a Laplace eigenfunction over a compact submanifold. Much like for the Weyl law, one can obtain improved estimates on period integrals given geometric or dynamical assumptions on the geodesic flow. While there are many results improving bounds on period integrals, there have been none which improve the remainder of the corresponding sum formula. In this talk, we discuss a recent joint work with Emmett Wyman. We show that an improvement to the remainder term of this sum formula reveals a lower-order oscillating term whose behavior can be described by the dynamics of the geodesic flow. Moreover, this oscillating second term illuminates bounds on period integrals.