CS153: Current Topics in Theoretical Computer Science
(Spring 2022)
Instructor: Chris
Umans
Office: Annenberg 311
Times: Tuesdays and Thursdays 1-2:25pm in Annenberg 213.
Office hours: Wednesdays 2-3pm in Annenberg 311.
Announcements:
- Solution sets for both problem sets have been posted.
Handouts:
Lecture notes:
- April 5, April 7: (txt)
- April 12,14,19,21: (txt)
Resources:
- Complexity of Bilinear Probelems (notes by Markus Blaser) (pdf)
- Outline of Basic Representation Theory (notes by Henry Cohn) (pdf)
Problem sets:
- Problem Set 1 (pdf) Solutions (pdf)
- Problem Set 2 (pdf) Solutions (pdf)
Papers we will read through together:
- H. Cohn and C. Umans. A Group-theoretic Approach to Fast Matrix Multiplication.
2003.
- H. Cohn, R. Kleinberg, B. Szegedy, and C. Umans. Group-theoretic Algorithms for
Matrix Multiplication. 2005.
- H. Cohn and C. Umans. Fast Matrix Multiplication using
Coherent Configurations. 2013.
- N. Alon, A. Shpilka, and C. Umans.
On Sunflowers and Matrix
Multiplication. 2013.
- J. Blasiak, T. Church, H. Cohn, J. Grochow, E. Naslund,
W. Sawin, and C. Umans.
On cap sets and the group-theoretic
approach to matrix multiplication. 2017.
- J. Blasiak, T. Church, H. Cohn, J. Grochow and
C. Umans. Which groups are amenable to proving exponent two for
matrix multiplication? 2017.
- J. Blasiak, H. Cohn, J. Grochow, K. Pratt, and
C. Umans. Matrix Multiplication via Matrix Groups. 2022.
Possible topics for presentation:
- Construction of optimal USPs via Coppersmith-Winograd hashing
(see me for a writeup).
- The sunflower paper above (which we didn't get to).
- Proof that no three Young Subgroups of S_n can beat exponent 3
(from "Amenable" paper above).
Presentation schedule:
- Antonio: May 24, coherent configurations paper
- Joe: May 26, groups, representations and communication complexity
- Rashida: May 26, slice-rank and instability of tensors
- David: May 31, reductions between MM and other linear
algebra problems
- Emile: May 31, C-W hashing
- Laura: June 2, Young subgroups of S_n
- Helen: June 2, sunflowers paper