Special Year Seminar

Vertex decomposition, introduced by Provan and Billera in 1980, is an inductive strategy for breaking down and understanding simplicial complexes. A simplicial complex that is vertex decomposable is shellable, hence Cohen--Macaulay. Through the...

Schubert Calculus studies cohomology rings in (generalized) flag varieties, equipped with a distinguished basis - the fundamental classes of Schubert varieties - with structure constants satisfying many desirable properties. Cotangent Schubert...

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...

Influential work of Hodge from the 1940s led the way in using Gröbner bases to combinatorially study the Grassmannian. We follow Hodge's approach to investigate certain subvarieties of the Grassmannian, called positroid varieties. Positroid...

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...