Related papers: The Work of R.E. Borcherds
We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika…
This paper gives an overview of Fred Cohen's work and is a summary of the talk which I gave during his 60th birthday conference, held at the University of Tokyo in July 2005.
This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.
An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…
In his striking 1995 paper, Borcherds found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of discriminant $-d$ evaluated at the modular $j$-function.…
The identities satisfied by two-dimensional chiral quantum fields are studied from the point of view of vertex algebras. The Cauchy-Jacobi identity (or the Borcherds identity) for three mutually local fields is proved and consequently a…
In this paper I shall try to sketch some typical aspects of Erich Lehmann's contributions to statistics through his research, his teaching, his service to the profession and his personality.
We explain some applications of bicategories in both classical and quantum field theory. This includes a modern perspective on some pioneering work of Max Kreuzer and Bert Schellekens on rational conformal field theory.
We formulate and prove the extension of the Rogers integral formula to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
In this article we prove a reciprocity law in number fields with odd class number that specializes to Scholz's reciprocity law over the rationals.
1. Translated by Thomas E. Cecil, Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA; E-mail address: [email protected] 2. Typed by Wenjiao Yan, School of Mathematical Sciences,…
This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…
This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in…
The concept of the elegant work introduced by Levai in Ref. [5] is extended for the solutions of the Schrodinger equation with more realistic other potentials used in different disciplines of physics. The connection between the present…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We recall major findings of a systematic investigation of the mathematization of the individual sciences, conducted by the author in Bielefeld some 35 years ago under the direction of Klaus Krickeberg, and confront them with recent…
The work studies some Difference equations, which are connected with Mejer's function.
This is the writeup of a talk given at the European Congress of Mathematics, Barcelona. It considers Picard-Lefschetz theory from the Floer cohomology viewpoint.