Related papers: Leaf schemes and Hodge loci

This is a survey article on the relationship between algebraic properties of diffeomorphism groups and homotopical properties of foliations, written for the Notices of the AMS.

This is a written-up version of eight introductory lectures to the Hodge theory of projective manifolds. The table of contents should be self-explanatory. The only exception is section 8 where I discuss, in a simple example, a technique for…

We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference…

Plant phenotyping refers to a quantitative description of the plants properties, however in image-based phenotyping analysis, our focus is primarily on the plants anatomical, ontogenetical and physiological properties.This technique…

Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of…

A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary transformations, such as translations, scalings, projections…

We extend the formalism of "log spaces" of arXiv:1507.06752 to topoi equipped with a sheaf of monoids, and discuss Deligne--Faltings structures and root stacks in this context.

Any algebraic connection on a vector bundle on a smooth complex algebraic curve determines an irregular class and in turn a fission tree at each puncture. The fission trees are the discrete data classifying the admissible deformation…

We investigate the notions of \emph{localization} and \emph{filtration} in the context of extended affine Lie algebras. Our primary objective is to develop a localization theory that facilitates the construction of meaningful local…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this article we study decompositions of cut loci over whose components the tangent cut loci fiber in…

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…

This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be…

This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical…

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…

Let $X$ be a smooth projective variety over the complex numbers and $S(d)$ the scheme parametrizing $d$-dimensional Lie subalgebras of $H^0(X,\mathcal{T} X)$. This article is dedicated to the study of the geometry of the moduli space…

We establish connectedness criteria for graphs associated to monomials in certain quotients of the mod 2 dual Steenrod algebra. We also investigate questions about trees and Hamilton cycles in the context of these graphs. Finally, we…

We present a decomposition of the generalized binomial coefficients associated with Jack polynomials into two factors: a stem, which is described explicitly in terms of hooks of the indexing partitions, and a leaf, which inherits various…

We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of group schemes and are in correspondence with graded Hopf algebra. In this setting, graded group varieties…

We show that closures of families of unitary local systems on quasiprojective varieties for which the dimension of a graded component of Hodge filtration has a constant value can be identified with a finite union of polytopes. We also…