相关论文: Perspectives on geometric analysis

Contribution to the Proceedings in honour of C.N. Yang, editor S-T Yau. To

This is the Preface to the special issue of 'International Journal of Geometric Methods in Modern Physics', v.3, N.1 (2006) dedicated to the 50th aniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation…

This survey article, in honor of G. Tian's 60th birthday, is inspired by R. Pandharipande's 2002 note highlighting research directions central to Gromov-Witten theory in algebraic geometry and by G. Tian's complex-geometric perspective on…

In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the…

The differential geometric aspects of Geometric Phases are reviewed.

Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…

This is an expanded version of my Shaw Prize Lecture delivered at the Chinese University of Hong Kong.

This article is a part of the report for the research project ``Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)'' in 1995, supported by the National Ministry of Education. There are…

This paper is based on the author's talk at the Grothendieck conference at Chapman university on 26-05-2022. It is not a survey of anabelian geometry but rather exposes some of the personal views and experiences of the author with the…

The year 2024 marks two anniversaries: The 70th anniversary of CERN and the 50th anniversary of the $J/\Psi$ discovery. At this occasion I have been asked to give review talks on the significance of these anniversaries. This article is an…

These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…

This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the…

The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.

This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt…

In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory. This geometrization, in addition of giving a nice insight on this result, offers us the occasion to investigate several points of…

This contribution follows the talk, given by F. Delduc at the conference SQS'2011 in Dubna, Russia (July 18-23, 2011). To a considerable extent it is a summary of known facts about the links between geometry and extended supersymmetry in…

This book is a regular textbook of analytical geometry covering vector algebra and its applications to describing straight lines, planes, and quadrics in two and three dimensions. The stress is made on vector algebra by using skew-angular…

In the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral…

These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.