Related papers: Engineered complete intersections: eliminating var…
We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensional subvarieties. As a consequence, we obtain the vanishing…
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at the Birch point. We compare this to log-barrier methods, with…
One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that…
This article introduces a general mesh intersection algorithm that exactly computes the so-called Weiler model (also called an arrangement) and that uses it to implement boolean operations with arbitrary multi-operand expressions, CSG…
This paper constructs a graded-commutative, associative, differential Transverse Intersection Algebra TIA {on the torus (in any dimension) with its cubical decomposition by using a probabilistic wiggling interpretation. This structure…
We study the topology of toric maps. We show that if $f\colon X\to Y$ is a proper toric morphism, with $X$ simplicial, then the cohomology of every fiber of $f$ is pure and of Hodge-Tate type. When the map is a fibration, we give an…
This article explores to which extent the algebro-geometric theory of rational descendant Gromov-Witten invariants can be carried over to the tropical world. Despite the fact that the tropical moduli-spaces we work with are non-compact, the…
We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on complete toric…
Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical…
The algebraic intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the algebraic intersection type…
This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…
Enumerative algebraic geometry deals with problems of counting geometric objects defined algebraically, An important class of enumerative problems is that of counting curves: given a class of curves in some projective variety defined by…
We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
An equivariant linear system on a toric variety is a linear system invariant under the torus action. We study the number of irreducible components of the complete intersection of general divisors from a fixed collection of equivariant…
A significant group of problems coming from the realm of Combinatorial Geometry can only be approached through the use of Algebraic Topology. From the first such application to Kneser's problem in 1978 by Lov% \'{a}sz \cite{Lovasz} through…
We define nondegenerate tropical complete intersections imitating the corresponding definition in complex algebraic geometry. As in the complex situation, all nonzero intersection multiplicity numbers between tropical hypersurfaces defining…
We present a classification algorithm for Calabi-Yau complete intersections arising from nef-partitions in fake weighted projective spaces, allowing us to determine all such complete intersections up to dimension five. Furthermore, we…