Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Eur, Christopher"'
For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory, tropical geometry, and the theory of total positivity. Bloch and Kar
Externí odkaz:
http://arxiv.org/abs/2410.11804
Positive geometries were introduced by Arkani-Hamed--Bai--Lam as a method of computing scattering amplitudes in theoretical physics. We show that a positive geometry from a polytope admits a log resolution of singularities to another positive geometr
Externí odkaz:
http://arxiv.org/abs/2403.04610
Autor:
Eur, Christopher, Larson, Matt
Hilbert polynomials have positivity properties under favorable conditions. We establish a similar "K-theoretic positivity" for matroids. As an application, for a multiplicity-free subvariety of a product of projective spaces such that the projection
Externí odkaz:
http://arxiv.org/abs/2311.11996
We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids introduced by Bouchet, which naturally arise in topological graph theory. The vant
Externí odkaz:
http://arxiv.org/abs/2311.09314
The moduli space of stable rational curves with marked points has two distinguished families of maps: the forgetful maps, given by forgetting some of the markings, and the Kapranov maps, given by complete linear series of $\psi$-classes. The collecti
Externí odkaz:
http://arxiv.org/abs/2308.12285
Autor:
Eur, Christopher
Tautological bundles of realizations of matroids were introduced in [BEST23] as a unifying geometric model for studying matroids. We compute the cohomologies of exterior and symmetric powers of these vector bundles, and show that they depend only on
Externí odkaz:
http://arxiv.org/abs/2307.04813
Delta-matroids are "type B" generalizations of matroids in the same way that maximal orthogonal Grassmannians are generalizations of Grassmannians. A delta-matroid analogue of the Tutte polynomial of a matroid is the interlace polynomial. We give a g
Externí odkaz:
http://arxiv.org/abs/2307.02550
Autor:
Eur, Christopher, Larson, Matt
Polymatroids are combinatorial abstractions of subspace arrangements in the same way that matroids are combinatorial abstractions of hyperplane arrangements. By introducing augmented Chow rings of polymatroids, modeled after augmented wonderful varie
Externí odkaz:
http://arxiv.org/abs/2301.00831
We prove that the number of tropical critical points of an affine matroid (M,e) is equal to the beta invariant of M. Motivated by the computation of maximum likelihood degrees, this number is defined to be the degree of the intersection of the Bergma
Externí odkaz:
http://arxiv.org/abs/2212.08173
Autor:
Eur, Christopher
Matroids are combinatorial abstractions of independence, a ubiquitous notion that pervades many branches of mathematics. June Huh and his collaborators recently made spectacular breakthroughs by developing a Hodge theory of matroids that resolved sev
Externí odkaz:
http://arxiv.org/abs/2211.05724