Machine Learning for Math and Physics
In this course, we will explore recent advancements in pure mathematics and physics that have emerged from interactions with the machine learning community. We will begin by reviewing the fundamentals of neural networks from a physics perspective before examining several successful applications of machine learning in predicting new mathematical and physical results. These developments include the discovery of new knot invariants, applications to the Poincaré conjecture, and insights into the String Landscape, among others. Additionally, we will discuss the role of large language models in advancing these fields.
Lecturer
Date
19th March ~ 9th July, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 14:20 - 16:05 | A14-203 | Zoom 15 | 204 323 0165 | BIMSA |
Syllabus
1. The concept of learning
2. Stat/Information theory background
3. Architecture
4. Supervised/unsupervised/reinfoeced/Bayesian/informed learning
5. Pretraining
6. RG flows and neural tangent kernel
7. ML applications to pure mathematics
8. ML applications to quantum field theory and string theory
9. Large language models
2. Stat/Information theory background
3. Architecture
4. Supervised/unsupervised/reinfoeced/Bayesian/informed learning
5. Pretraining
6. RG flows and neural tangent kernel
7. ML applications to pure mathematics
8. ML applications to quantum field theory and string theory
9. Large language models
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
My education begain in Russia where I learned math and physics at Moscow Insitute of Physics and Technology. I started my research career as a theoretical physicist after obtaining my PhD from University of Minnesota in 2012. At first, my research focus was drawn to various aspects of supersymmetric gauge theories and string theory. However, I have always been drawn to pure abstract mathematics since my student days. Since around 2017 I have been a full time mathematician.
My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory. More recently I began to study number theory and how it is connected to other branches of mathematics.
If you are postdoc or a graduate student in Beijing area and you are interested in working with me contact me via email.
My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory. More recently I began to study number theory and how it is connected to other branches of mathematics.
If you are postdoc or a graduate student in Beijing area and you are interested in working with me contact me via email.