A Survey into Lower Bounding Cohn & Umans Matrix Multiplication

Bounding matrix multiplication runtime has been an active area of research since 1969 when Strassen
showed ω ≤ 2.81. In 2003, Cohn and Umans produced a matrix multiplication framework and
conjectured ω = 2. However, a concrete lower bound greater than 2 has never been given. More works
over the year by Alman and Williams focus on lower bounding matrix multiplication using various
methods including Cohn and Umans’. However, no concrete lowerbound for this method has been given.
In this research, we initially aim to give a lower bound tighter than 2 to Cohn & Umans method. Our
literature review shows that there are no existing techniques to achieve this task. Therefore, this talk
summarizes and surveys the current literature regarding this topic.