Topics in modern homotopy theory II
Two main (independent) topics for this semester will be the \Lambda-algebra and simplicial localization.
1. We will study the \Lambda-algebra from the perspective of the mod-p unstable Adams spectral sequence. If time permits, we will discuss the questions related to Koszhul duality between the \Lambda-algebra and the Steenrod algebra.
2. We will start with the classical works of Dwyer and Kan on simplicial localization and then move to a discussion of simplicial localization as a model for \infty-categories.
1. We will study the \Lambda-algebra from the perspective of the mod-p unstable Adams spectral sequence. If time permits, we will discuss the questions related to Koszhul duality between the \Lambda-algebra and the Steenrod algebra.
2. We will start with the classical works of Dwyer and Kan on simplicial localization and then move to a discussion of simplicial localization as a model for \infty-categories.
讲师
Fedor Pavutnitskiy
日期
2024年03月06日 至 05月21日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二 | 10:40 - 15:05 | Online | ZOOM 07 | 559 700 6085 | BIMSA |
修课要求
category theory, homological algebra, simplicial homotopy theory
课程大纲
1. Lower central series of a simplicial group
2. Simplicial Lie algebras
3. The unstable Adams spectral sequence and applications
4. Introduction of simplicial localization
5. Hammock localization
6. Dwyer-Kan localization for \infty-categories
2. Simplicial Lie algebras
3. The unstable Adams spectral sequence and applications
4. Introduction of simplicial localization
5. Hammock localization
6. Dwyer-Kan localization for \infty-categories
参考资料
1. E. Curtis "Simplicial homotopy theory"
2. W. Dwyer, D. Kan "Simplicial localization of categories"
2. W. Dwyer, D. Kan "Simplicial localization of categories"
听众
Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
Fedor Pavutnitskiy主要研究单纯同伦论及其在path homology中的应用，以及与群和李代数相关的同调代数，同时对机器学习在现代数学中的应用感兴趣。