Introduction to topos quantum theory

A topos is a mathematical structure which resembles the category of sets, and furthermore has a notion of localization. This structure has an internal logic associated to it, in which true-false logic may be replaced by multi-valued logic. Topos quantum theory uses this to give a contextual formulation of quantum mechanics. I will give an introduction to these ideas with examples.

Lecturer

William Donovan

Date

27th February ~ 6th April, 2023

Location

Weekday	Time	Venue	Online	ID	Password
Monday	13:30 - 15:05	1129B	ZOOM 04	482 240 1589	BIMSA
Thursday	10:40 - 12:15	1129B	ZOOM 04	482 240 1589	BIMSA

Prerequisite

Some basic knowledge of quantum mechanics and category theory. Background in logic or algebraic/differential geometry would be helpful.

Syllabus

Review of quantum theory, Hilbert spaces, Kochen-Specker theorem; review of category theory, functors, natural transformations; presheaves, sections, definition of topos, sieves, Heyting algebras; topos state space, spectral presheaf, propositions, daseinisation; truth values, probability.

Reference

Flori, A First Course in Topos Quantum Theory

Audience

Graduate

Video Public

Yes

Notes Public

Yes

Language

English

Lecturer Intro

Will Donovan joined Yau MSC, Tsinghua U in 2018. Since 2021 he is an Associate Professor, and Adjunct Associate Professor at BIMSA. His focus is geometry, in particular applying ideas from physics and noncommutative algebra to study varieties, using tools of homological algebra and category theory. He studied at Cambridge U, completed his PhD at Imperial College London, and was postdoctoral researcher at Edinburgh U, UK. From 2014-18 he was research fellow at Kavli IPMU, U Tokyo, where he is now Visiting Associate Scientist. His work is published in journals including Communications in Mathematical Physics and Duke Mathematical Journal. He is supported by China Thousand Talents Plan, and received a Japan Society for Promotion of Science Young Scientist grant award.