A class of tensors, called "concise (m,m,m)-tensors of
minimal border rank", play an important role in proving upper
bounds for the complexity of matrix multiplication. For that reason
Problem 15.2 of "Algebraic Complexity Theory" by Bürgisser...
This colloquium will explore some fundamental issues in the
mathematics of plasmas, focusing on the stability and instability
of solutions to Vlasov-type equations, which are crucial for
describing the behavior of charged particles in a plasma. A...
A dot-product proof is a simple probabilistic proof system in
which the verifier decides whether to accept an input vector based
on a single linear combination of the entries of the input and a
proof vector. I will present constructions of linear...
Chapter 14 of the classic text "Computational Complexity" by
Arora and Barak is titled "Circuit lower bounds: complexity
theory's Waterloo". I will discuss the lower bound problem in the
context of algebraic complexity where there are barriers...
The free group algebra appears often as a major tool in dealing
with problems about free groups. It is also a lovely object for its
own sake, featuring many analogies with the free group: for
example, it satisfies an analog of the Nielsen-Schreier...
