Special Year Seminar

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...

Multi-variate residues on Grassmannians G(k,n) and moduli spaces M0,n are ubiquitous in the study of scattering amplitudes; they provide a powerful and essential tool. Amenable theories include the biadjoint scalar, NLSM, Yang-Mills, gravity and N=4...

A classical construction associates a Poincare duality algebra to a homogeneous polynomial on a vector space. This construction was used to give a presentation for cohomology rings of complete smooth toric varieties by Khovanskii and Pukhlikov and...

In the third talk, I will concentrate on inequalities for linear extensionsof finite posets.  I will start with several inequalities which do have a combinatorial proof.  I will then turn to Stanley's inequality and outline the proof why its defect...

In the second talk, I will concentrate on polynomial inequalities and whether the defect (the difference of two sides) has a combinatorial interpretation.  For example, does the inequality  x2+y2≥2xy

  have a combinatorial proof and what does that...

In the first talk, I will give a broad survey of classical inequalities that arise in enumerative and algebraic combinatorics.  I will discuss how these inequalities lead to questions about combinatorial interpretations, and how these questions...