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60
GLOBAL ASPECTS OF THE GEOMETRY OF SURFACES
, 907
"... Abstract. Several open problems related to the behavior of the monoid of effective divisors and the nef cone for smooth projective surfaces over an algebraically closed field are discussed, motivating and putting into historical context concepts such as Mori dream spaces, Seshadri constants and the ..."
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Cited by 10 (5 self)
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and the resurgence of homogeneous ideals in polynomial rings. Some recent work on these topics is discussed along with the problem of which ordinary powers of homogeneous ideals contain given symbolic powers of those ideals. Exercises, with solutions, are included. I. Lecture: Bounded Negativity I.1. Introduction. A
2003), “Globalization and Its Challenges
 American Economic Review
"... I stand here with deeply conflicting emotions. I am honored to be delivering this prestigious lecture. I am profoundly sad that Rudi Dornbusch, who should have delivered the Ely Lecture, died in July last year and that I am here in his place. So I would like to start by talking about Rudi. Rudi was ..."
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Cited by 63 (0 self)
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I stand here with deeply conflicting emotions. I am honored to be delivering this prestigious lecture. I am profoundly sad that Rudi Dornbusch, who should have delivered the Ely Lecture, died in July last year and that I am here in his place. So I would like to start by talking about Rudi. Rudi
The geometry of dynamical triangulations
 Lecture Notes in Physics m50
, 1997
"... The express purpose of these Lecture Notes is to go through some aspects of the simplicial quantum gravity model known as the Dynamical Triangulations approach. Emphasis has been on lying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct ..."
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Cited by 46 (8 self)
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distinct mathematical fields ranging from global riemannian geometry, moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can establish in this field
Lectures on black holes and linear waves
"... Igor Rodnianski� These lecture notes, based on a course given at the Zürich Clay Summer School (June 23–July 18 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this problem stems from its relationship to the nonli ..."
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Cited by 31 (2 self)
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Igor Rodnianski� These lecture notes, based on a course given at the Zürich Clay Summer School (June 23–July 18 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this problem stems from its relationship to the non
RICHARD T. ELY LECTURE Globalization and Its Challenges
"... I stand here with deeply conflicting emotions. I am honored to be delivering this prestigious lecture. I am profoundly sad that Rudi Dornbusch, who should have delivered the Ely Lecture, died in July last year and that I am here in his place. So I would like to start by talking about Rudi. Rudi was ..."
Abstract
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I stand here with deeply conflicting emotions. I am honored to be delivering this prestigious lecture. I am profoundly sad that Rudi Dornbusch, who should have delivered the Ely Lecture, died in July last year and that I am here in his place. So I would like to start by talking about Rudi. Rudi
Wave equations on Lorentzian manifolds and quantization
, 2007
"... In General Relativity spacetime is described mathematically by a Lorentzian manifold. Gravitation manifests itself as the curvature of this manifold. Physical fields, such as the electromagnetic field, are defined on this manifold and have to satisfy a wave equation. This book provides an introducti ..."
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Cited by 44 (0 self)
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an introduction to the theory of linear wave equations on Lorentzian manifolds. In contrast to other texts on this topic [Friedlander1975, Günther1988] we develop the global theory. This means, we ask for existence and uniqueness of solutions which are defined on all of the underlying manifold. Such results
Lectures on topological quantum field theory
 Proceedings of the Meeting on Integrable Systems, Quantum Groups and Quantum Field Theory
, 1992
"... What follows are lecture notes about Topological Quantum Field Theory. While the lectures were aimed at physicists, the content is highly mathematical in its style and motivation. The subject of Topological Quantum Field Theory is young and developing rapidly in many directions. These lectures are n ..."
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Cited by 4 (0 self)
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are not at all representative of this activity, but rather reflect particular interests of the author. Our theme is locality and gluing laws. The idea that global quantities can be computed from local formulas is an old one in topology and geometry. So too are formulas which express the change in a global
Topics in Combinatorial Differential Topology and Geometry
, 2004
"... Many questions from a variety of areas of mathematics lead one to the problem of analyzing the topology or the combinatorial geometry of a simplicial complex. We will see a number of examples in these notes. Some very general theories have been developed for the investigation of similar questions fo ..."
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. In the third lecture, we show that discrete Morse theory is a very natural tool for the study of some questions in complexity theory. Much of the study of global differential geometry is concerned with the relationship between the geometry of a Riemannian manifold and its topology. One long conjectured, still
Lecture Notes Geometric Wave Equations
"... In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed including a detailed treatment of the Ca ..."
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Cited by 1 (0 self)
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In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed including a detailed treatment
Lectures on mean curvature flows in higher codimensions
, 2008
"... Mean curvature flows of hypersurfaces have been extensively studied and there are various different approaches and many beautiful results. However, relatively little is known about mean curvature flows of submanifolds of higher codimensions. This notes starts with some basic materials on submanifo ..."
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Cited by 6 (1 self)
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on submanifold geometry, and then introduces mean curvature flows in general dimensions and codimensions. The related techniques in the so called “blowup ” analysis is also discussed. At the end, we present some global existence and convergence results for mean curvature flows of twodimensional surfaces
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