Fast matrix multiplication is one of the most fundamental problems in algorithm research.
The exponent of the optimal time complexity of matrix multiplication is usually denoted by ω …

In this work, we prove limitations on the known methods for designing matrix multiplication
algorithms. Alman and Vassilevska Williams recently defined the Universal Method, which …

In this paper we further explore the recently discovered connection by Björklund and Kaski
[STOC 2024] and Pratt [STOC 2024] between the asymptotic rank conjecture of Strassen …

In the light bulb problem, one is given as input vectors x_1,...,x_n,y_1,...,y_n∈{-1,1\}^d which
are all uniformly random. They are all chosen independently except for a planted pair …

Strassen's asymptotic rank conjecture [Progr. ‍Math. ‍120 ‍ (1994)] claims a strong
submultiplicative upper bound on the rank of a three-tensor obtained as an iterated …

The exponent $\sigma (T) $ of a tensor $ T\in\mathbb {F}^ d\otimes\mathbb {F}^
d\otimes\mathbb {F}^ d $ over a field $\mathbb {F} $ captures the base of the exponential …

Karppa & Kaski (2019) proposed a novel``broken" or``opportunistic" matrix multiplication
algorithm, based on a variant of Strassen's algorithm, and used this to develop new …

Our main limitation result is that a large class of tensors generalizing the Coppersmith-
Winograd tensors (the family of tensors used in all record-holding algorithms for the past 30+ …

As proposed by Karppa and Kaski (in: Proceedings 30th ACM-SIAM Symposium on Discrete
Algorithms (SODA), 2019) a novel “broken" or" opportunistic" matrix multiplication algorithm …