skip to main content

Title: Algorithms for orbit closure separation for invariants and semi-invariants of matrices
Authors:
;
Award ID(s):
1900460
Publication Date:
NSF-PAR ID:
10273520
Journal Name:
Algebra & Number Theory
Volume:
14
Issue:
10
Page Range or eLocation-ID:
2791 to 2813
ISSN:
1937-0652
Sponsoring Org:
National Science Foundation
More Like this
  1. We consider the general non-vanishing, divergence-free vector fields defined on a domain in $3$ -space and tangent to its boundary. Based on the theory of finite-type invariants, we define a family of invariants for such fields, in the style of Arnold’s asymptotic linking number. Our approach is based on the configuration space integrals due to Bott and Taubes.
  2. We focus on various dynamical invariants associated to monomial correspondences on toric varieties, using algebraic and arithmetic geometry. We find a formula for their dynamical degrees, relate the exponential growth of the degree sequences to a strict log-concavity condition on the dynamical degrees and compute the asymptotic rate of the growth of heights of points of such correspondences.