Related papers: Rational Homotopy Theory
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
This is an introduction to: (1) the enumerative geometry of rational curves in equivariant symplectic resolutions, and (2) its relation to the structures of geometric representation theory. Written for the 2015 Algebraic Geometry Summer…
This paper has been withdrawn due to errors found by authors. A correct version of this paper is published in: Tomasz M. Rusin, Wlodek Zawadzki, "Quantum theory of symmetric screening in the Hartree approximation", Phys. stat. sol. (b) 243,…
Homotopy methods have proven to be a powerful tool for understanding the multitude of solutions provided by the coupled-cluster polynomial equations. This endeavor has been pioneered by quantum chemists that have undertaken both elaborate…
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
The purpose of this paper is to formulate a number of conjectures giving a rather complete description of the tautological ring of M_g and to discuss the evidence for these conjectures.
We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.
We review the special theory of relativity kinematics and dynamics as well as the general theory of relativity under the aspect of logic.
We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra of distributive monochromatic bi-operads.
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…
This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul…
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal…
This paper gives a first step towards developing synthetic differential geometry within homotopy type theory. Its model theory will be discussed in a subsequent paper.
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.