Related papers: Recent progress on the Minimal Model Program for f…

This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space…

Given a finite unbranched covering of a nonsingular projective scheme we analyse the morphism between moduli spaces of sheaves induced by pullback. We have a closer look at cyclic coverings and, in particular, at canonical coverings of…

simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added,…

In this paper, we provide toric descriptions for various foliation singularities on toric varieties, especially for non-dicritical singularities and F-dlt singularities. We then show that the toric foliated minimal model program works by…

We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…

This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that on the one hand is of great significance in theoretical…

This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.

A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…

The conformal field theory on a Z_N-surface is studied by mapping it on the branched sphere. Using a coulomb gas formalism we construct the minimal models of the theory.

We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable…

We find all $P$-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces Jan Steven's list [Manuscripta Math. 1993] of the numbers…

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of…

Let W be a planar 3-web defined on a neighborhood of a point M. We call "symmetry of W around M" any local diffeomorphism which fixes M and maps each foliation of W to a (not necessarily the same) foliation of W. We say that it is a simple…

This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter…

In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a…

In this paper, we employ the loop group method to study the construction of minimal Lagrangian surfaces in the complex projective plane for which the surface is contractible. We present several new classes of minimal Lagrangian surfaces in…

We study non-compact surfaces obtained by gluing strips $\mathbb{R}\times(-1,1)$ with at most countably many boundary intervals along some these intervals. Every such strip possesses a foliation by parallel lines, which gives a foliation on…

In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new…

We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.

Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…