Related papers: Differential Characters and Geometric Chains
In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
To a digraph with a choice of certain integral basis, we construct a CW complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph as introduced in \cite{GLMY}. The homotopy type of the CW…
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…
In this talk I give an introduction and present some recent progress towards understanding the cohomology rings of character varieties of Riemann surfaces, such as the proof of the $P=W$ conjecture and the computation of the…
Let $M$ be a $n$-dimensional complex manifold and $f,g:M\to M$ two distinct holomorphic self-maps. Suppose that $f$ and $g$ coincide on a globally irreducible compact hypersurface $S\subset M$. We show that if one of the two maps is a local…
We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…
Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
We study the q-characters and modular data of exceptional W-algebras and give several examples and applications. We establish equality of q-characters and modular data between certain boundary W-algebras, leading in particular to a largely…
We build a bridge between geometric group theory and topological dynamical systems by establishing a dictionary between coarse equivalence and continuous orbit equivalence. As an application, we give conceptual explanations for previous…
We give a Chern-Weil map for the Gel'fand-Fuks characteristic classes of Haefliger-singular foliations, those foliations defined by smooth Haefliger structures with dense regular set. Our characteristic map constructs, out of singular…
The goal of this paper is to explain how basic properties of perverse sheaves sometimes translate via Riemann-Hilbert correspondences (in both characteristic $0$ and characteristic $p$) to highly non-trivial properties of singularities,…
A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the…
Just as $\Cstar$ principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
Texture characterization is a key problem in image understanding and pattern recognition. In this paper, we present a flexible shape-based texture representation using shape co-occurrence patterns. More precisely, texture images are first…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
This is a survey article whose main goal is to explain how many components of the character variety of a closed surface are either deformation spaces of representations into the maximal compact subgroup or deformation spaces of certain…
This paper continues our study of the sheaf associated to K\"ahler differentials in the cdh-topology and its cousins, in positive characteristic, without assuming resolution of singularities. The picture for the sheaves themselves is now…