Related papers: Rational Homotopy Theory
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.
In this paper we outline a setup for Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical perspectives are considered.
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
This survey is intended as an invitation to the theory of stable $\infty$-categories, addressed primarily to mathematicians working in the representation theory of algebras and related subjects.
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
In this paper we propose to use a relative variant of the notion of the \'{e}tale homotopy type of an algebraic variety in order to study the existence of rational points on it. In particular, we use an appropriate notion of homotopy fixed…
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.
For a semisimple complex algebraic group $G$ we determine the rational cohomology and the Hodge-Tate structure of the moduli stack ${\mathscr B}un_{G,X}$ of principal $G$-bundles over a connected smooth complex projective variety $X$ of…
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…
We survey some topics in ${\mathbb A}^1$-homotopy theory. Our main goal is to highlight the interplay between ${\mathbb A}^1$-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various…
Some speculative preliminary ideas relating matrix theory and cosmology are discussed.
The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].
The primary goal of this paper is to find a homotopy theoretic approximation to moduli spaces of holomorphic maps Riemann surfaces into complex projective space. There is a similar treatment of a partial compactification of these moduli…
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics,…
In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.
This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.