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.
讲师
日期
2023年02月27日 至 04月06日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 13:30 - 15:05 | 1129B | ZOOM 04 | 482 240 1589 | BIMSA |
| 周四 | 10:40 - 12:15 | 1129B | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
Some basic knowledge of quantum mechanics and category theory. Background in logic or algebraic/differential geometry would be helpful.
课程大纲
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.
参考资料
Flori, A First Course in Topos Quantum Theory
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
2018年加入YMSC。自2021起担任YMSC的副教授以及BIMSA的兼职副教授。他的研究重点是几何，特别是利用同调代数和范畴论的工具，将物理学和非交换代数中的思想用于代数簇的研究。他曾就读于剑桥大学，在伦敦帝国理工学院获得博士学位，并在英国爱丁堡大学担任博士后。2014-2018年，他在东京大学Kavli IPMU担任研究员，现在是该校的访问副研究员。他的论文发表在Communications in Mathematical Physics，Duke Mathematical Journal等期刊上。他入选了海外高层次人才计划，并获得了日本科学促进会青年科学家奖。