相关论文: The Work of R.E. Borcherds

Book Review of Quantum Field Theory by Lewis H. Ryder. An observation on Ryder's derivation of Dirac equation is made. The review ends as, "A rare combination of a thorough understanding and appreciation of the essential logical structure…

Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is where tomorrow's breakthroughs are quietly prepared. In…

We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.

This is an English translation of Moufang's notes "Grundlagen der Geometrie" at the University of Frankfurt in 1948, with added notes by the translator.

Work in progress concerning alternative formalizations of arithmetic.

The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblematic figure of Analysis and Partial Differential Equations in…

Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.

While the ``hierarchy of science'' has been widely analysed, there is no corresponding study of the status of subfields within a given scientific field. We use bibliometric data to show that subfields of mathematics have a different…

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. In this paper, we establish for O(p,2) an adjointness result between Borcherds' singular theta lift and the Kudla-Millson…

We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss…

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).

Invited contribution to the inaugural issue of {\em Physics Educator.}

The Borcherds Phi-function is the automorphic form on the moduli space of Enriques surfaces characterizing the discriminant locus. In this paper, we give an algebro-geometric construction of the Borcherds Phi-function.

Germany has become a major country of immigration, as well as a research powerhouse in Europe. As Germany spends a higher fraction of its GDP on research and development than most countries with advanced economies, there is an expectation…

We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.

Roger Carter (1934--2022) was a very well known mathematician working in algebra, representation theory and Lie theory. He spent most of his mathematical career in Warwick. Roger was a great communicator of mathematics: the clarity,…

This is an unchanged version of an unpublished, ``state of the art'' survey given at a conference held in Stuttgart in 2001 to celebrate the 100th birthday of Richard Brauer. This text was recently quoted in several papers on the…

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…

The current Special Issue of The Annals of Statistics contains three invited articles. Javier Rojo discusses Erich's scientific achievements and provides complete lists of his scientific writings and his former Ph.D. students. Willem van…

Remarks on mathematical proof and the practice of mathematics.