Title: Group-theoretic Algorithms for Matrix Multiplication

Abstract:
We develop fast matrix multiplication algorithms based on the theory of 
finite group representations, according to the paradigm introduced by Cohn 
and Umans in 2003. The fastest of these algorithms runs in O(n^2.41) 
operations.  We present two conjectures, either of which (if resolved 
affirmatively) would imply that the exponent of matrix multiplication is 
equal to 2. 

This is joint work with Henry Cohn, Robert D. Kleinberg, and Christopher 
Umans, in FOCS 2005.  The paper is available on-line at
http://theory.csail.mit.edu/~rdk/papers/CKSU05.pdf

A news article about this work is available at
http://www.siam.org/pdf/news/174.pdf