Organizers
Bin Gui(归斌), Tsinghua University
Zhengwei Liu(刘正伟), Tsinghua University
Jinsong Wu(吴劲松), BIMSA
Abstract
The focus of this workshop is to delve into the profound mathematical architecture that underpins modern quantum theory. Our exploration centers on the intricate tapestry of mathematical frameworks developed to describe, analyze, and predict quantum phenomena. This includes, but is not limited to, the rigorous study of operator algebras and C*-algebras, which provide the foundational language for quantum mechanics and statistical mechanics, formalizing observables, states, and their evolution.
A key area of discussion will be vertex operator algebras (VOAs), algebraic structures that are not only pivotal in the representation theory of infinite-dimensional Lie algebras but also serve as the mathematical backbone of two-dimensional conformal field theories (CFT). CFT itself represents a cornerstone of modern theoretical physics, with deep connections to critical phenomena in statistical mechanics and string theory. The workshop will naturally extend into the broader realm of quantum field theory (QFT), examining its mathematical formulations, such as algebraic QFT and constructive QFT, which strive to put this immensely successful physical framework on solid mathematical ground.
Beyond foundational physics, we will explore the mathematical dialogue with quantum information theory. Here, concepts from operator theory, functional analysis, and probability theory converge to quantify entanglement, characterize quantum channels, and analyze quantum algorithms and cryptography. The role of probability theory is twofold: it is intrinsic to the axiomatic interpretation of quantum mechanics and provides essential tools for studying stochastic processes in open quantum systems and measurement theory. By bringing together these interconnected disciplines, the workshop aims to foster cross-pollination of ideas, address outstanding mathematical challenges, and illuminate the deep structural unity between abstract mathematics and the quantum description of nature.
