**CS153: Current Topics in Theoretical Computer Science
(Spring 2016) **

Instructor: Chris Umans

Office: Annenberg 311

Times: Tu/Th 1:00-2:25 in Annenberg 314

Office hours: email me

Announcements:

- Problem set 2 has been posted. It is due May 24.

Handouts:

- Syllabus (pdf)

Lectures:

- Lecture 1: introduction; models of algebraic computation
- Lecture 2: bilinear circuits and tensor rank; Strassen's algorithm
- Lecture 3: border rank
- Lecture 4: Asymptotic Sum Inequality
- Lecture 5: groups and the group-theoretic approach
- Lecture 6: examples satisfying the triple product property
- Lecture 7: the strong USP construction and conjecture
- Lecture 8: the two families construction and conjecture

Problem sets:

Papers:

- 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.
- N. Alon, A. Shpilka and C. Umans. On Sunflowers and Matrix Multiplication. 2011.
- H. Cohn and C. Umans. Fast Matrix Multiplication using Coherent Configurations. 2013.
- A. Stothers. On the complexity of matrix multiplication. 2010.
- V. V. Williams. Multiplying matrices in O(n 2.373) time. 2014.

Surveys and course notes:

- M. Blaser. Complexity of Bilinear Problems. 2009.

Possible papers for presentation:

- More to come...