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...
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...
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...
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...
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...
