Related papers: Sketch for a Theory of Constructs
We construct a map from knots to (abstract) 2-knots which can be extended to higher dimensions; this map is the natural "knot" counterpart for "braid" theory of groups $G_{n}^{k}$.
In these notes we generalize the theory of graphical functions from scalar theories to theories with spin.
This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…
In this paper, we give a necessary condition for a diagram to represent the trivial knot.
This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
These are notes from a basic course in Several Complex Variables
We show a method in constructing algebraic cycles via intersection theory. It leads to a proof of the Lefschetz standard conjecture.
Particular solutions of the Benney equations are constructed. Their properties are discussed.
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
We produce a new, shorter construction of a minor-universal planar graph.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
A Short Course on Frame Theory.