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.
Lecturer
Fedor Pavutnitskiy
Date
6th March ~ 21st May, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 10:40 - 15:05 | Online | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
category theory, homological algebra, simplicial homotopy theory
Syllabus
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
Reference
1. E. Curtis "Simplicial homotopy theory"
2. W. Dwyer, D. Kan "Simplicial localization of categories"
2. W. Dwyer, D. Kan "Simplicial localization of categories"
Audience
Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
No
Language
English
Lecturer Intro
I'm working in simplicial homotopy theory and its applications in path homology and homological algebra related to groups and Lie algebras. I'm also interested in applications of deep learning in contemporary mathematics.