Related papers: Height inequalities and canonical class inequaliti…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
Plenary talk at the conference, LATTICE 99, held in Pisa, Itay from June 29 to July 3, 1999.
We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes,…
These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
This is an expanded version of the author's talk at the third annual meeting of International Consortium of Chinese Mathematicians held at USTC in December 2020. In this expository article, we give a survey on joint works with Hosono, Lian,…
An extended text of the talk given at the conference ``2001: A Spacetime Odyssey'', to be published in the Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, 21-25 May…
These are notes for a Ph.D.\ course I held at SISSA, Trieste, in the Winter 2025. We review well-known topics in Riemannian geometry where Lie groups play a fundamental role. Part of the theory of compact connected Lie groups, their…
This article contains a collection of problems contributed during the course of the conference.
This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to…
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…
We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.
Absract (Invited talk at the X DAE High Energy Physics symposium in December 1992, held at Tata Institute of Fundamental Research, Bombay)
These lectures review certain topological defects and aspects of their cosmology. Unconventional material includes brief descriptions of electroweak defects, the structure of domain walls in non-Abelian theories, and the spectrum of…
Informal seminar notes explaining the ideas in math.DS/0411344 and math.DS/0411345.
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
Extra dimensions provide a new window on a number of problems faced by the Standard Model. The following provides an introduction to this very broad subject aimed at experimental graduate students and post-docs based on a lecture given at…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
A summary is presented of the more theoretical aspects of the presentations made at Hyperon~99. In addition, some material is covered which was not presented at the symposium but which I feel is pertinent to the main theme of hyperons…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…