Manifolds, Analysis, and Applications
This will be an in-person class. The purpose of this class is to introduce fundamental concepts of differential geometry and its application to other fields, so that people in physics, biology, applied math, or machine learning (where differential geometry is applied) can have a rigorous introduction to the subject. The main topics will include manifolds, vector bundles, connections, curvature, introduction to geometric flows, and applications. This will be supplemented by learning fundamental tools of geometric analysis. Anyone is welcome even though it is designed for math advanced (senior) undergrads and early (freshman) grad students
Lecturer
Puskar Mondal
Date
5th March ~ 4th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 14:20 - 16:05 | A7-101 | Zoom 15 | 204 323 0165 | BIMSA |
Prerequisite
basic topology, real analysis
Syllabus
To be updated.
Reference
Differential Geometry by Cliff. Taubes
Manifolds and Differential Geometry by J.M Lee
Lecture notes on Differential Geometry, R. Schoen, S-T Yau (this is mostly for the more advanced geometric analysis part)
We will not follow any particular textbook (otherwise, there's no point in teaching)
Manifolds and Differential Geometry by J.M Lee
Lecture notes on Differential Geometry, R. Schoen, S-T Yau (this is mostly for the more advanced geometric analysis part)
We will not follow any particular textbook (otherwise, there's no point in teaching)
Audience
Advanced Undergraduate
, Graduate
Video Public
No
Notes Public
Yes
Language
English
Lecturer Intro
Puskar Mondal is currently a postdoctoral fellow at CMSA (dept. of Mathematics) and a lecturer at the Math department at Harvard University. His mentor is Prof. Shing-Tung Yau. Before this, he was a Ph.D. student at Yale university where he worked on Mathematical General Relativity under the supervision of Prof. Vincent Moncrief.