Langlands Correspondence for Loop Groups
by Edward Frenkel
Publisher: Cambridge University Press 2007
Number of pages: 393
This book provides an excellent detailed review of an important aspect of the geometric Langlands program, namely, the role of representation theory of affine Kac-Moody algebras (or loop algebras). It provides clear and insightful introductions to such notions as vertex algebras, the Langlands dual group, connections on the punctured disc, representation theory of loop algebras, etc.
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by Krassimir Atanassov - Erhus Univ Pr
A collection of 27 Smarandache's problems which the autor solved by 1999. 22 problems are related to different sequences, 4 problems are proved, modifications of two problems are formulated, and counterexamples to two of the problems are constructed.
by A. Genestier, B.C. Ngo
The goal of these lectures is to explain the representability of moduli space abelian varieties with polarization, endomorphism and level structure, due to Mumford and the description of the set of its points over a finite field, due to Kottwitz.
by Richard Dedekind - The Open Court Publishing
This is a book combining two essays: 'Continuity and irrational numbers' - Dedekind's way of defining the real numbers from rational numbers; and 'The nature and meaning of numbers' where Dedekind offers a precise explication of the natural numbers.
by Douglas Ulmer - arXiv
The focus is on elliptic curves over function fields over finite fields. We explain the main classical results on the Birch and Swinnerton-Dyer conjecture in this context and its connection to the Tate conjecture about divisors on surfaces.