Special Year Seminar

K-theory arose in the 1950s from Grothendieck’s formulation of the Riemann-Roch theorem – that is, from attempts to calculate spaces of sections of vector bundles on a variety X via intersection theory on X.  An equivariant version was introduced...

A remarkable result of Brändén and Huh tells us that volume polynomials of projective varieties are Lorentzian polynomials. The dual notion of covolume polynomials was introduced by Aluffi by considering the cohomology classes of subvarieties of a...

The ring of symmetric functions has a linear basis of Schur functions $s_{\lambda}$ indexed by partitions $\lambda = (\lambda_1 \geq \lambda_2 \geq \ldots \geq 0 )$. Littlewood-Richardson coefficients $c^{\nu}_{\lambda, \mu}$ are the structure...

We show that various classical theorems of linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a general result that involves a tiling of a closed oriented surface by...

We present a combinatorial approach to the Deligne-Mumford-Knudsen compactification of the moduli space of n distinct points on the projective line $P^1$. The idea is to choose a totally symmetric embedding of the orbits of generic points into a...

A real plane algebraic curve C is called expressive if its defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of C. We give a necessary and sufficient criterion for expressivity (subject...