We study the class of Lorentzian polynomials. The class contains homogeneous stable
polynomials as well as volume polynomials of convex bodies and projective varieties. We …

I will tell two interrelated stories illustrating fruitful interactions between combinatorics and
Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter …

In this paper, we study lower tail probabilities of the height function $\mathfrak {h}(M, N) $ of
the stochastic six-vertex model. We introduce a novel combinatorial approach to …

Chromatic symmetric functions are well-studied symmetric functions in algebraic
combinatorics that generalize the chromatic polynomial and are related to Hessenberg …

Let k be an arbitrary field, P= P km 1× k⋯× k P kmp be a multiprojective space over k, and
X⊆ P be a closed subscheme of P. We provide necessary and sufficient conditions for the …

We study several properties of multihomogeneous prime ideals. We show that the
multigraded generic initial ideal of a prime has very special properties, for instance, its …

We introduce bubbling diagrams and show that they compute the support of the
Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that …

We describe the twisted $ K $-polynomial of multiplicity-free varieties in a multiprojective
setting. More precisely, for multiplicity-free varieties, we show that the support of the twisted …

We prove that if a level set of a degree n general inverse σ k equation f (λ 1,⋯, λ n):= λ 1⋯ λ
n−∑ k= 0 n− 1 ck σ k (λ)= 0 is contained in q+ Γ n for some q∈ R n, where ck are real …

Grothendieck polynomials G w of permutations w∈ S n were introduced by Lascoux and
Schützenberger (CR Acad Sci Paris Sér I Math 295 (11): 629–633, 1982) as a set of …