Related papers: Building Mixed Hodge Structures
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
Every countable structure has a sentence of the infinitary logic $\mathcal{L}_{\omega_1 \omega}$ which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought…
We study the monodromies and the limit mixed Hodge structures of families of complete intersection varieties over a punctured disk in the complex plane. For this purpose, we express their motivic nearby fibers in terms of the geometric data…
This piece has been written for local, educational purposes. If you are like me searching for the right words to explain your fascination with high Tc superconductivity to the outside world, you might find something useful in this text.
The purpose of this thesis is to use the language of orbifold groupoids to describe the geometry and topology of orbifolds, highlighting advantages and disadvantages of this language as they arise.
The first author in recent work with D. Gay developed the notion of a Morse structure on an open book as a tool for studying closed contact 3-manifolds. We extend the notion of Morse structure to extendable partial open books in order to…
In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.
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…
The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. Also, space limitation does not…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
This is the first of the two articles where we determine the higher smooth surgery structure sets of complex projective spaces (up to some extension problems) and the forgetful map to their topological versions in low dimensions. In this…
We consider a hypersurface in $\mathbb{C}^n$ with an isolated singular point at the origin, and study the mixed Hodge structure of the stalk of its intersection cohomology complex at the origin. In particular we express the dimension of…
In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts…
The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.
We propose a generalization of the notion of ${\bf R}$-split mixed Hodge structure by defining a ${\bf R}$-splitting level for mixed Hodge structures. This is a discrete invariant taking values in positive integers and equal to 0 for ${\bf…
This is a technical introduction to the paper "Extension of twisted Hodge metrics for Kahler morphisms" by the authors.
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
A construction similar to Hagge's construction for circles through the orthocentre is shown to apply for any point.
This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers of spaces and towers of spectra.
In this article we survey some of the recent developments in the structure theory of set addition.