Previous Special Year Seminar

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...

Lecture Series Framework:  A unifying framework for F1-geometry, tropical schemes and matroid theory. In this series of 3 lectures, I will present a recent approach towards F1-geometry and its links to tropical geometry, matroid theory, Lorentzian...

The study of the topology of hyperplane arrangement complements has long been a central part of combinatorial algebraic geometry. I will talk about intersection pairings on the twisted (co)homology for a hyperplane arrangement complement, first...

I will motivate the study of the Schubert variety of a pair of linear spaces via Kempf collapsing of vector bundles. I'll describe equations defining this variety and how this yields a simplicial complex determined by a pair of matroids which...

For an embedded stable curve over the real numbers we introduce a hyperplane arrangement in the tangent space of the Hilbert scheme. The connected components of its complement are labeled by embeddings of the graph of the stable curve to a compact...

A sequence of nonnegative real numbers $a_1, a_2, \ldots, a_n$, is log-concave if $a_i^2 \geq a_{i-1}a_{i+1}$ for all $i$ ranging from 2 to $n-1$. Examples of log-concave inequalities range from inequalities that are readily provable, such as the...