A valuation is a finitely additive measure on the class of all
convex compact subsets of $R^n$. Over the past two decades, a
number of structures has been discovered on the space of
translation invariant smooth valuations. Recently, these
findings...
The theme of the 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 variety X...
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...
