相关论文: Potpourri

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…

The purpose of this note is to start the systematic analysis of cofinal types of topological groups.

We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…

This essay recounts my personal journey towards a deeper understanding of the mathematical foundations of algorithmic music composition. I do not spend much time on specific mathematical algorithms used by composers; rather, I focus on…

We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

In this note we briefly survey and propose some open problems related to isoparametric theory.

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

This short note contains elementary evaluations of some Euler sums.

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

The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.

$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…

The aim of these notes is to explain main ideas of the theory of complements. Basically we will follow Shokurov's work alg-geom/9711024.

This manuscript summarizes a series of three lectures on interactions of neutrinos . The lectures begin with a pedagogical foundation and then explore topics of interest to current and future neutrino oscillation and cross-section…

These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…