Showing papers by "Michael Atiyah published in 2000"
Book•
04 Jan 2000
TL;DR: In this paper, the authors present a review of the 20 and 21 centuries of number theory, analysis, and mathematical physics with respect to the Riemann zeta function and its applications in mathematics.
Abstract: Number theory, transcendence and Diophantine geometry in the next millennium by A. Baker and G. Wustholz Harmonic analysis and combinatorics: How much may they contribute to each other? by J. Bourgain Back to Riemann by S.-S. Chern Noncommutative geometry and the Riemann zeta function by A. Connes Polynomials, vanishing cycles and Floer homology by S. K. Donaldson The two cultures of mathematics by W. T. Gowers Ten problems by V. F. R. Jones An algebraic integration by D. Kazhdan Mathematics: The right choice? by F. Kirwan On some challenging problems in nonlinear partial differential equations by P.-L. Lions Real world turbulence and modern applied mathematics by A. J. Majda Mathematics as profession and vocation by Yu. I. Manin Problems and conjectures in rigidity theory by G. Margulis A glimpse into symplectic geometry by D. McDuff Rational curves on algebraic varieties by S. Mori The dawning of the age of stochasticity by D. Mumford Mathematical physics of the 20 and 21 centuries by R. Penrose Limitations to regularity by K. F. Roth Conversations on mathematics with a visitor from outer space by D. Ruelle Some problems in number theory, analysis and mathematical physics by P. Sarnak Mathematical problems for the next century by S. Smale Positivity problems and conjectures in algebraic combinatorics by R. P. Stanley On the future of mathematics/physics interaction by C. Vafa Twenty years of number theory by A. Wiles Magic, mystery, and matrix by E. Witten Review of geometry and analysis by S.-T. Yau Polymathematics: Is mathematics a single science or a set of arts? by V. I. Arnold Mathematics and computing by P. D. Lax The theme of adic variation by B. Mazur.
182 citations
TL;DR: In this paper, a large $N$ duality in the context of type IIA strings with supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIAs in M-theory.
Abstract: We show how a recently proposed large $N$ duality in the context of type IIA strings with ${\cal N}=1$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $G_2$ holonomy manifolds and an $S^3$ flop are the key ingredients in this derivation.
60 citations
Posted Content•
TL;DR: A brief account of K-theory written in honour of Friedrich Hirzebruch is given in this article, where the author presents an account of the Ktheory and its history.
Abstract: A brief account of K-theory written in honour of Friedrich Hirzebruch
41 citations
Posted Content•
TL;DR: In this article, a cohomological study is made of an equivariant map betwen the configuration space of n points in space and the flag manifold of U(n) for a given configuration space.
Abstract: A cohomological study is made of an equivariant map betwen the configuration space of n points in space and the flag manifold of U(n).
5 citations