Record: Yes

Level: Graduate

Language: English

Prerequisite

Some representation theory or algebraic geometry would be helpful.

Abstract

Quiver representations are a useful tool in diverse areas of algebra and geometry. Recently, they have furthermore been used to describe and analyze neural networks. I will introduce quivers, their representations, and a range of applications, including to the theory of machine learning.

Reference

Syllabus

1. Quivers, quiver representations, path algebras, modules;

2. continuous groups, Grassmannians, homogeneous spaces, quiver flag varieties, moduli spaces;

3. neural networks, data flow, activation functions, gradient flow;

4. universal approximation theorems, further topics.

Lecturer Intro

Will Donovan joined Yau MSC, Tsinghua U in 2018. Since 2021 he is an Associate Professor, and Adjunct Associate Professor at BIMSA. His focus is geometry, in particular applying ideas from physics and noncommutative algebra to study varieties, using tools of homological algebra and category theory. He studied at Cambridge U, completed his PhD at Imperial College London, and was postdoctoral researcher at Edinburgh U, UK. From 2014-18 he was research fellow at Kavli IPMU, U Tokyo, where he is now Visiting Associate Scientist. His work is published in journals including Communications in Mathematical Physics and Duke Mathematical Journal. He is supported by China Thousand Talents Plan, and received a Japan Society for Promotion of Science Young Scientist grant award.

Lecturer Email: donovan@tsinghua.edu.cn

TA: Dr. Hamed Adami, hamed.adami@bimsa.cn