Special Year 2024-25: Algebraic and Geometric Combinatorics - 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...

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...

Multi-variate residues on Grassmannians $G(k,n)$ and moduli spaces $M_{0,n}$ 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...

The moduli space of pointed rational curves has a natural action of the symmetric group permuting the marked points.  In this talk, we will present a combinatorial formula for the induced representation on the cohomology of the moduli space, along...

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...