相关论文: Why everyone should know number theory

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent…

In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skeptical majority. In a muted form this split applies to the authors of this note. When we learned that the only mathematically sound…

Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…

These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers…

We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…

We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…

This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…

This paper is intended to offer a pedagogical treatment of cosmological modeling and inflationary cosmology. In recent years, inflation has become accepted as a standard scenario making predictions that are testable by observations of the…

The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…

These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.

These are the notes for my 2017 Takagi lectures on DT counts of curves in algebraic threefolds. We discuss the fundamentals of the subject, its origins, open questions, and certain recent advances.

Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…

These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.

The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…

In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…