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:

• Problem Set 1: (pdf)
• Problem Set 2: (pdf)

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...