Related papers: The Picard Scheme
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…
In this paper we give another proof of the Chudnovsky formula for calculating $\pi$ - a proof in detail with means of basic complex analysis. With the exception of the tenth chapter, the proof is self-contained, with proofs provided for all…
We construct a category, $\Omega$, of which the objects are pointed categories and the arrows are pointed correspondences. The notion of a "spec datum" is introduced, as a certain relation between categories, of which one has been given a…
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
We present some new sharp constructions for the Szemer\'{e}di-Trotter theorem. These constructions generalize previous work of Erd\H{o}s, Elekes, Sheffer and Silier, Guth and Silier, and the author. In the past, arguments showing the…
We introduce the notion of primitive elements in arbitrary truncated $p$-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the "points of exact order $N$,"…
In this work, we introduce new combinatorial objects called Dyck tableaux, which present a natural insertion algorithm. These tools may be useful to describe statistics which are relevant in the study of the physical model named PASEP.
In his famous work, "Measurement of a Circle," Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern…
The objective of this article is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
Theory of Probability is distinguished by several high-level philosophical attitudes, some stressed by Jeffreys, some implicit. By reviewing these we may recognize the importance in this work in the historical development of statistics.…
This is an attempt at an elementary exposition, with examples, of the theory of motivic integration developed by R. Cluckers and F. Loeser, with the view towards applications in representation theory of p-adic groups.
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
This very short paper presents a novel approach to Euler's formula without presupposing it. The paper reclaims the rightful place of the formula at the heart of calculus.
Grothendieck polynomials are important objects in the study of the $K$-theory of flag varieties. Their many remarkable properties have been studied in the context of algebraic geometry and tableaux combinatorics. We explore a new tool,…
An introduction to the methods and ideas of Chiral Perturbation Theory is presented in this talk. The discussion is illustrated with some phenomenological predictions that can be compared with available experimental results.
We establish a valuative version of Grothendieck's section conjecture for curves over p-adic local fields. The image of every section is contained in the decomposition subgroup of a valuation which prolongs the p-adic valuation to the…
Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663--688, 2005.]. This article considers the basic properties that a…