Related papers: Toric Topology. Chapter 2: Combinatorial structure…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
This a collection of about 100 exercises. It could be used as a supplement to the book Koll\'ar--Mori: Birational geometry of algebraic varieties.
Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
In this paper we survey results and recent progresses on the equivariant bordism classification of 2-torus manifolds and unitary toric manifolds.
These lecture notes are based on lectures given by the author at the summer school "Arrangements in Pyr\'en\'ees" in June 2012. We survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we…
We construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold. All necessary topological definitions and combinatorial constructions are given and the statement is…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a…
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component.…
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a…
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations.…
Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this thesis we explore this correspondence to classify smooth lattice…
In this paper we build an Orlik-Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of…
This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…
Combinatorial and topological aspects of monoids with an absorbing element and their associated algebras are considered. Phd thesis.
We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.
We present a construction of noncommutative double mirrors to complete intersections in toric varieties. This construction unifies existing sporadic examples and explains the underlying combinatorial and physical reasons for their…
We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and locally convex $\widetilde{\C}$-linear topology. In this…