相关论文: Potpourri, 11

These notes discuss in an informal manner the construction and some properties of 1- and 2-gerbes. They are mainly based on the author's previous work in this area, which is reviewed here, and to some extent improved upon. The main emphasis…

We expand upon some topics reviewed and sketched in a book to appear with more details, embellishments, and some new material of a speculative nature.

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…

These informal notes briefly discuss Fourier inversion in terms of Gauss--Weierstrass kernels and summability.

We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.

In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.

A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.

Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.

This short note contains an elementary observation in response to the recent posting arXiv:1707.06593v1, which studies the Lipschitz extension modulus to $n$ additional points. We bound this modulus in terms of the well-studied Lipschitz…

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

These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…

Work in progress concerning alternative formalizations of arithmetic.

The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.

We give an elementary description of the space of formal periods of a mixed motive. This allows for a simplified reformulation of the period conjectures of Grothendieck and Kontsevich-Zagier. Furthermore, we develop a machinery which in…

This is mostly* a non-technical exposition of the joint work arXiv:1212.0373 with Caporaso and Payne. Topics include: Moduli of Riemann surfaces / algebraic curves; Deligne-Mumford compactification; Dual graphs and the combinatorics of the…

These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.

A collection of short expository essays by the author on various topics in quantum mechanics, quantum cosmology, and physics in general.