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...
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 theme of the third lecture is the notion of points over F1,
the field with one element. Several heuristic computations led to
certain expectations on the set of F1-points: for example the Euler
characteristic of a smooth projective complex...
The second lecture features the nuts and bolts of the invariants
from first lecture, which we call foundations. We explain the
structure theorem for foundations of ternary matroids, which is
rooted in Tutte's homotopy theorem. We show how this...
