相关论文: Geometry and the Imagination in Minneapolis

This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric…

The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional…

This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the…

An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.

Invited talk delivered at the International Conference on General Relativity and Cosmology (ICGC), Ahmedabad, India; 13 - 18 December 1991. To appear in its proceedings.

These notes grew out of several introductory talks I gave during the years 2003--2005 on motivic integration. They give a short but thorough introduction to the flavor of motivic integration which nowadays goes by the name of geometric…

These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is…

This is an overview of merging the techniques of Riesz space theory and convex geometry.

These are the notes corresponding to the course given at the IAS-Park City graduate summer school in July 2007.

This is a colloquium style pedagogical introduction to the paradigm of large extra dimensions. To be published in the Proceedings of the Workshop "Crossing the boundaries: Gauge dynamics at strong coupling," (May 14 - 17, 2009,…

This paper agrees basically with the talk of the author at the workshop "Homological Mirror Symmetry and Applications", Institute for Advanced Study, Princeton, March 2007.

This short survey has been prepared in connection with the workshop on discrete metric spaces and their applications at Princeton, August, 2003, and tries to convey some of the ways that one might look at functions on metric spaces in…

The purpose of this thesis is to convey the basic concepts of information geometry and its applications to non-specialists and those in applied fields, assuming only a first-year undergraduate background in calculus, linear algebra, and…

This introductory text arises from a lecture given in G\"oteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically inclined reader wishing to explore a synthesis of ideas…

This article contains reminiscences of the collaborative work that Richard Arnowitt and I did together which stretched over many years and encompasses several areas of particle theory. The article is an extended version of my talk at the…

This is an expanded version of a three-hour minicourse given at the winterschool Winterbraids IV held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We…

These notes are a record of lectures given in the Workshop on Connections Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012. The lectures were meant as an introduction to current research problems related to fat…

The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work…

These are the lecture notes from my 2014 PCMI graduate summer school lectures. In these lectures, we'll study simple models of materials from several different perspectives: geometry (packing problems), information theory (error-correcting…

This is a revised version of a tutorial lecture that I presented at the \`Ecole de Physique des Houches on July 26-31 2020. Topics include Non-parametric Information Geometry, the Statistical bundle, exponential Orlicz spaces, and Gaussian…