Sci. June 23, 2014. 20 : 1. , H. Blaine Lawson, Jr. and Maire-Louise Michelsohn, Spin Geometry (New Jersey, USA: Prince University Press, 1989). , Jürgen Jost, Riemannian Geometry and Geometric Analysis (Heidelberg: Springer, 2008). Dusa McDu { vita, February 6, 2017 5 July 2015: Introductory lecture at IHES Summer School, Paris: Transversality problems in symplectic geometry. It follows that is invariant under the flow of the Hamilton equations which are familiar from classical mechanics: We already said earlier that at every regular point of the Hamiltonian vector field is tangent to the level sets of . , Lev Landau and Evgeny Lifschitz, Quantum Mechanics: Non-Relativistic Theory (Oxford: Butterworth-Heinemann, 1981). Inflating s to s - "Dusa McDuff and symplectic geometry." Karsten Grove, The inevitable presence of singular spaces in Riemannian geometry; Lisa Jeffrey, Volumes of moduli spaces of flat connections on Riemannian surfaces; Jun Li, Anti-self-dual connections on SU(2) bundles over algebraic surfaces; Dusa McDuff, Symplectic 4-manifolds; Clifford Taubes, Anti-self dual conformal structures in 4 dimensions She is particularly interested in issues connected with the position of women in mathematics, and currently serves on the MSRI Board of Trustees. There are also various results related to blow-ups and blow-downs. Math. , Holger Wendland, Numerical Linear Algebra: An Introduction (Cambridge: Cambridge University Press, 2017). The modification of the metric follows from the fact that multiplying a Riemannian metric by a function multiplies the volume form by . This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry. 12, 427 – 433 (1959). If is a Hamiltonian with the associated regular level set, then one can see that. , Martin Sadd, Elasticity: Theory, Applications, and Numerics (USA: Academic Press, 2009). As a corollary of the previous statement, every smooth manifold has a distance function whose metric topology is equivalent to the induced topology. Inst. In this note we show that one open 4-dimensional ellipsoid embeds symplectically into another if and only if the ECH capacities of the first are no larger than those of the second. J-holomorphic Curves and Symplectic Topology (with D. Salamon) (Colloq. Take Thurston’s symplectic Kähler -manifold . Here is the complete text: jholsm.pdf, Erratum to Third edition of Introduction to Symplectic Topology, Sept. 2017  pdf. , Dusa McDuff, ‘The moment map for circle actions on symplectic manifolds’, Journal of Geometrical Physics, 5, 149 – 160 (1988). , Lev Landau and Evgeny Lifschitz, Quantum Mechanics: Non-Relativistic Theory (Oxford: Butterworth-Heinemann:, 1981). Let us suppose given by the level set of the smooth Hamiltonian is compact and non-empty. visit the project's GitHub page to open an issue. This theorem states that there is no symplectic embedding which takes a standard -ball with unit radius into a cylinder whose base space is a closed disc with -area 154. , John M. Lee, Introduction to Smooth Manifolds (New York: Springer, 2003). Indeed one often talks about symplectic topology. In particular, we construct an interesting metric for the symplectic diffeomorphism groups, which is related, but, Abstract We prove packing stability for rational symplectic manifolds. Dusa McDuff, Dietmar Salamon. , Bryan Rynne and Martin Youngson, Linear Functional Analysis (London: Springer, 2008). , Maxim Kazaryan, Sergei Lando and Victor Prasolov, Algebraic Curves: Towards Moduli Spaces (Switzerland: Springer, 2018). Rev. Lectures on Symplectic Topology, Park City 1997: This text has the merit of being fairly short and readable, but the reader should beware of certain errors and omissions detailed here. $$\tilde \omega _k , k \geqq 0$$ , John Morgan and Gang Tian, Ricci Flow and the Poincaré Conjecture (Providence, Rhode Island: American Mathematical Society, 2007). Tim Perutz , University of Texas, Austin and IAS. Comments: This is the paper written … Geometry, Topology, and Physics for Raoul Bott (Cambridge, Massachusetts: International Press, 1994). , Louis Billera, Susan Holmes and Karen Vogtmann, ‘Geometry of the space of phylogenetic trees’, Advances in Applied Mathematics 27, 733 – 767 (2001). You may see some authors write to emphasise the dependence on the connection, but we will drop this, as it is implicit. , Charlotte Froese Fischer, Georgio Tachiev and Andrei Irimia, ‘Relativistic energy levels, lifetimes, and transition probabilities of the sodium-like to argon-like sequences’, Atomic Data and Nuclear Data Tables, 92(5), 607 – 812 (2006). A trip to Moscow in 1969 was a turning point for Dusa McDuff, then a promising young mathematician who was yet to find her mathematical path. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. , Richard Schoen and Shing-Tung Yau, ‘Proof of the Positive Mass Theorem. This minimum number obviously has to be at least from elementary calculus, because any function will have a distinct local maximum and local minimum. , Frances Kirwan, ‘Symplectic quotients of unstable Morse strata for normsquares of moment maps’ (2018), arXiv:1802.09237v1. Dusa McDuff is a mathematician who has produced seminal and ground-breaking work on symplectic geometry. The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. Some features of the site may not work correctly. Symplectic diffeomorphisms are then simply the diffeomorphisms which preserve this symplectic invariant, hence we see that the four basic strands of the subject influence each other. First notions Symplectic geometry is an even dimensional geometry. Organized by Kenji Fukaya, Dusa McDuff, and John Morgan January 2 – June 30, 2014. , Maryam Mirzakhani, ‘Weil-Petersson volumes and intersection theory on the moduli space of curves’, J. Amer. Together with Dietmar Salamon,  she has written several foundational books on symplectic topology as well as many research articles. , Jean-Pierre Serre, Topics in Galois Theory (Boston: Jones and Bartlett Publishers, 1992). MATHEMATICAL CONGRESS OF THE AMERICAS, GUANAJUATO, MEXICO, AUGUST 2013. Symplectic Structures— A New Approach to Geometry Dusa McDuff Introduction Symplectic geometry is the geometry of a closed skew-symmetric form. , Michael Powell, Approximation Theory and Methods (Cambridge: Cambridge University Press, 1981). Reid), and also at Moscow University (1968-69 with I.M.Gelfand). Perspectives on topology and geometry of 4-manifolds, Dubrovnik, Croatia, June 2016. , Henry Cohn, Abhinav Kumar, Stephen Miller, Danylo Radchenko and Maryna Viazovska, ‘The sphere packing problem in dimension ’, Annals of Mathematics, 185(3), 1017 – 1033 (2017). The creativity they brought to mathematics was a revelation to McDuff, who had just finished her second year as a … Ana Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in Mathematics 1764, Springer-Verlag. Dusa McDuff and Dietmar Salamon Oxford Graduate Texts in Mathematics. (2) 54, 1 – 37 (1951). , Miles Reid, Undergraduate Algebraic Geometry (Cambridge: Cambridge University Press, 2010). Eckhard Meinrenken, lecture notes on Symplectic Geometry, on his website. , Edward Witten, ‘A New Proof of the Positive Energy Theorem’, Commun. This book, together with McDuff and Salamon’s Introduction to Symplectic Topology and their many other contributions, has been a great help to both junior and senior symplectic geometers. Dusa McDuff FRS CorrFRSE (born 18 October 1945) is an English mathematician who works on symplectic geometry.wikipedia. , Yvonne Choquet-Bruhat, ‘Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires’, Acta Math. Math. , Erwin Kreyszig, Introductory Functional Analysis with Applications (USA: John Wiley & Sons, 1978). Found inside – Page iiThe intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). , Julia Robinson, ‘An iterative method of solving a game’, Annals of Mathematics 54, 296 – 301 (1951). 84, 223 – 238 (1982). , Maryam Mirzakhani, ‘Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces’, Invent. We have already mentioned symplectic geometry a few times, so we should probably explain the topological side of things a bit more. is surjective. Weinstein proposed his conjecture for all hypersurfaces of contact type and it was subsequently proved by Viterbo that every hypersurface of contact type in has a closed characteristic. , Seiju Ohashi, Tetsuya Shiromizu and Sumio Yamada, ‘The Riemannian Penrose inequality and a virtual gravitational collapse’, Physical Review D. 80(4) (2009). Introduction to Symplectic Topology —Ana Cannas da Silva. Horst Janson, History of Art (New Jersey, USA: Prentice Hall Publishing, 1991). J. This can be proved with a short computation. Dusa McDuff is a mathematician who brought symplectic geometry to the attention of the mathematical world. Providence, Rhode Island : American Mathematical Society ; [Stony Brook, New York] : Simons Center for Geometry and Physics, [2019] Mathematical surveys and monographs no. , Claire Voisin, ‘On the homotopy types of compact Kähler and complex projective manifolds’, Inventiones Math. Summer Graduate School. The conjecture relates the minimum number of fixed points of a Hamiltonian symplectomorphism on a closed manifold to Morse theory157. Issue edi­ted by S. Ak­bu­lut, T. Önder, and R. J. Stern. Vol. 28, 289 – 294 (1971). Leroy P … It turns out that the key to characterizing symplectomorphisms is to use the non-squeezing theorem to define a symplectic invariant which is continuous with respect to the topology. Problemes de plongement. Abstract 6.45 KB application/pdf: Show Detail. , Mikhail Gromov, ‘Pseudo-holomorphic curves in symplectic manifolds’, Invent. Dusa McDuff and Dietmar Salamon, "Introduction to Symplectic Topology", 3rd Edition, 2017. Volume 88, 141 – 225 (1952). The specific statement of the conjecture is that the Reeb vector field of such a hypersurface must have at least one periodic orbit. , Dirk Kreimer, ‘Multi-valued Feynman graphs and scattering theory’, arXiv:1807:00288v3 (2018). Early life and education. In the section on linear complex structures particular emphasis is placed on the homotopy equivalence between the space of symplectic forms and the space of linear complex structures. In the context of almost complex structures, McDuff proved that for a compact connected symplectic -manifold which contains a symplectically embedded -sphere with an intersection number defined by the positive definite inner product , we have that is the blow-up of a rational or ruled symplectic -manifold. , Paul Cohn, Basic Algebra: Groups, Rings and Fields (Trowbridge: Springer, 2003). , Dusa McDuff, ‘Rational and ruled symplectic -manifolds’, Journal of the American Mathematical Society, 3, 679 – 712 (1990). D. from the University of California, Berkeley, USA. , Alexander Litvak, Konstantin Tikhomirov and Nicole Tomczak-Jaegermann, ‘Small ball probability for the condition number of random matrices’, arXiv:190-08655vs (2019). A number of new constructions have appeared in the development of these global studies. , Olga Oleinik, ‘Construction of a generalized solution of the Cauchy problem for a quasi-linear equation of first order by the introduction of ‘vanishing viscosity’’, Uspekhi Matematicheskikh Nauk, 14 (2(86)), 159 – 164 (1959). Found inside – Page 175Lectures on Gromov invariants for symplectic 4-manifolds DuSa MCDUFF* Department of Mathematics State University of New York at Stony Brook Stony Brook, ... NY Joint Symplectic Geometry Seminar Meets in Math 520 : 1:15 p.m.: Mu-Tao Wang (Columbia) Mean curvature flows of Lagrangian submanifolds and isotopy problems in symplectic geometry. In a paper on circle actions, McDuff proved that a symplectic circle on a closed -manifold is Hamiltonian if and only if it has fixed points, also providing an example of a symplectic, non-Hamiltonian circle action on a compact symplectic -manifold with fixed points162. , Carolyn Gordon, Dorothee Schueth and Craig Sutton, ‘Spectral isolation of bi-invariant metrics on compact Lie groups’, Ann. Math. , Zi-Cai Li, Yimin Wei, Yunkun Chen and Hung-Tsai Huang, ‘The method of fundamental solutions for the Helmholtz equation’, Applied Numerical Mathematics. , Sofia Kovalevskaya, ‘Sur le problème de la rotation d'un corps solide autour d'un point fixe’, Acta Mathematica, 12: 177 – 232 (1899). Everything on the right hand side is evaluated for . Informally speaking, a contact structure can be viewed as a field of hyperplanes which could not be further from integrability. It is a result of Whitney (the embedding theorem) that every smooth -manifold has a proper smooth embedding into . Margaret Dusa Waddington was born in London, England, on 18 October 1945 to noted biologist Conrad Hal Waddington and Edinburgh architect Justin … They introduce symplectic topology at various levels of sophistication, starting from the easiest. The inverse function theorem states that if and are smooth manifolds, , and a smooth map between the two manifolds such that the pushforward is a bijection, then there exist connected neighbourhoods of and of such that the restriction of from to is a diffeomorphism. Darboux’s theorem says that locally all symplectic … 135, 510 – 536 (2019). 65, 45 – 76 (1979). It lives on even dimensional spaces, and measures the sizes of 2-dimensional objects rather than the 1-dimensional lengths and angles that are familiar from Euclidean and Riemannian geometry. Third Edition. Columbia University The symplectic embedding problem Geometry and Topology Seminar 26th January 2021, 2:00 pm – 3:00 pm Zoom seminar, if interested, please email one of the organisers to gain access to the Zoom link , Hans-Jürgen Stöckmann, Quantum Chaos: An Introduction (Cambridge: Cambridge University Press, 2006). , Max Koch, Christiane Lechner, Fabian Reuter, Karsten Köhler, Robert Mettin and Werner Lauterborn, ‘Numerical modelling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using OpenFOAM’, Computers and Fluids. Published by the AMS under the auspices of the International Mathematical Union, this book features the best and brightest stars in math reflecting on where math has been and where it might go in the next century. , D. V. Evtushinsky et al., ‘Momentum-resolved superconducting gap in the bulk of from combined ARPES and SV’, New Journal of Physics, 11(5), 55069 (2009). , Rick Miranda, Algebraic Curves and Riemann Surfaces (USA: American Mathematical Society, 1995). Found insideSuitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. , Maryam Mirzakhani, ‘Growth of the number of simple closed geodesics on hyperbolic surfaces’, Ann. This talk will discuss some recent developments concerning the question of when a 4-dimensional ellipsoid can be symplectically embedded in a ball. Nash’s embedding theorem is a similar result for Riemannian manifolds149. Start with a regular value of a smooth Hamiltonian . Nauk. The second chapter introduces the basic concepts of symplectic topology in the linear algebra setting, such as symplectic vector spaces, the linear symplectic group, Lagrangian subspaces, and the Maslov index. This manifold is a quotient , where is the discrete affine group generated by the unit translations along the -axes along with a transformation. The … In symplectic topology, we study the global structure of a symplectic manifold and the non-local behaviour of symplectomorphisms which are far from the identity. , Paolo Aluffi and Matilde Marcolli, ‘Feynman motives of banana graphs’, Communications in Number Theory and Physics, 3(1) (2008). . , Glen Bredon, Topology and Geometry (New York: Springer-Verlag, 1993). 100% (1/1) C. Humphrey Caroline Caroline Waddington. Request PDF | On Mar 1, 2021, Felix Schlenk published Dusa McDuff and Symplectic Geometry | Find, read and cite all the research you need on ResearchGate flaws. , Fernando Albiac and Nigel Kalton, Topics in Banach Space Theory (Switzerland: Springer, 2016). , Mary Cartwright, ‘On functions which are regular and of finite order in an angle’, Proc. Now just use well-known properties of the exponential map which can be looked up in any textbook of differential geometry and evaluate for a pair of vectors and a point in the unit ball153. Over the past number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. Catherine Cannizzo is a Research Assistant Professor at the Simons Center for Geometry and Physics at Stony Brook University, USA. 80, 381 – 402 (1981). She holds a Ph. Vol. Helvetici, 71, 70 – 97 (1996). Thus symplectic geometry is essentially topological in nature. Applications of Symplectic Geometry (Cambridge 1994) (S. K. Donaldson and C. B. Thomas, eds. , on a compact manifold , Michael Peskin and Daniel Schroeder, An Introduction to Quantum Field Theory (USA: Westview Press, 1995). Dusa McDuff, Professor of Mathematics, Columbia University,Dietmar Salamon, Professor of Mathematics, ETH Zurich Dusa McDuff was born in London, UK, in 1945. This proof of the Darboux theorem was originally suggested by Moser. Theor. This immediately implies that. , Olga Oleinik, ‘On the uniqueness of the generalized solution of the Cauchy problem for a nonlinear system of equations occurring in mechanics’, Usp. , Constantine Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge: Cambridge University Press, 1992). , Sergiu Klainerman, Igor Rodnianski, and Jérémie Szeftel, ‘The resolution of the bounded curvature conjecture in general relativity’, Séminaire Laurent Schwartz. In 1978, she joined the faculty of the Department of Mathematics at SUNY Stony Brook, where she was awarded the title of Distinguished Professor in 1998. Differential Geometry and Lie Groups I & II, by Jean Gallier and Jocelyn Quaintance; Differential Topology, by Victor Guillemin and Alan Pollack; Lectures on Symplectic Geometry, by Ana Cannas da Silva; Introduction to Symplectic Topology, by Dusa McDuff and Dietmar Salamon A point in the other manifold is said to be a regular value of if every point of the set is a regular point. This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Transl. , Allen Hatcher, Algebraic Topology (Cambridge: Cambridge University Press, 2009). This follows from Darboux’s theorem, which states that every symplectic form on is locally diffeomorphic to the standard form on Euclidean . DOI: 10.1090/NOTI2238 Corpus ID: 226278001. Math., 107(4) 969 – 997 (1985). Dusa has received numerous prizes and recognitions for her work. One can often use the desirable properties of the exponential map to obtain proofs for other lemmas and theorems. , Marcel Lesieur, Turbulence in Fluids (Dordrecht, The Netherlands: Kluwer Academic Publishers, 1997). Fellow of the Association for Women in Mathematics. E 93, 033121 (2016). Dusa McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. Some features of the site may not work correctly. To prove that the exponential map is a diffeomorphism onto a neighbourhood of , we need to calculate the derivative at the zero vector of the tangent space. , Peter Olver, Introduction to Partial Differential Equations (Cham, Switzerland: Springer, 2016). J. 3009 Broadway, Milbank Hall 332, New York, NY 10027 | 212.854.3577, Copyright © 2021 Barnard College | Columbia University, Helen Lyttle Kimmel '42 Professor of Mathematics, 612 Mathematics Building on Columbia campus. Introduction to Symplectic Topology, 2nd edition, with D. Salamon (Oxford University Press, 1998) pdf  A third edition of this book is under preparation. May 11. , Benoit Fresse, Homotopy of Operads and Grothendieck-Teichmüller Groups: The Applications of Rational Homotopy Theory Methods (Providence. , Brian Bowditch, A Course on Geometric Group Theory (Japan: Mathematical Society of Japan, 2006). Soc., 1970). 11 offers from $29.99. Lecture 1: Recent results and open questions 1 1.1. Also, consider a bundle such that the fibre at every point is the orthogonal complement of for a submanifold of Euclidean space: this is called the normal bundle to the submanifold148. Available for Zoom meetings anytime after Sept. 30. WHAT IS SYMPLECTIC GEOMETRY? She holds a Ph. To discuss mistakes or suggest improvements, please send an e-mail at hollis.williams@warwick.ac.uk The derivative of is then a linear self-map for the tangent space: By the identification with Euclidean space, the map defines a local coordinate chart for neighbourhood of , where is mapped to . This second edition has been significantly revised and expanded, with new references and examples added and theorems included or revised. Math. 2 Recent advances In this section I will list some of the most significant advances in symplectic geom-etry of the past 4 years. —Dusa McDuff & Dietmar Salamon. (A level sets approach was crucial in the Huisken-Ilmanen proof of the Riemannian Penrose inequality which we mentioned earlier). A sequence of these embeddings can be shown to be, In this paper we show that symplectic maps have surprising topological properties. The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. A: Math. This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course. To be clear, a smooth -dimensional vector bundle is a pair of smooth manifolds (known as the total space) and a base space , along with a surjective map called the projection map, such that every fibre of over a point is equipped with the structure of a vector space. DUSA MCDUFF Abstract. Vosko, ‘Ground states of Ca− and Sc – from two theoretical points of view’, Physical Review Letters, 59, 2263 – 2266 (1987). Dusa McDuff and symplectic geometry. Paris 248, 3519 – 3521 (1959). , Filip Rindler, Calculus of Variations (Cham, Switzerland: Springer, 2018). , Leila Schneps and P. Lochak, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups (Cambridge: Cambridge University Press, 1997). In equation form: One way of seeing that is true is to do a short computation with the exponential map. , Andriy Bondarenko, Danylo Radchenko and Maryna Viazovska, ‘Optimal asymptotic bounds for spherical designs’, Annals of Mathematics, 178(2), 443 – 452 (2013). Dusa McDuff is Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College, USA. C. R. Acad. Soc., 17, 557 – 593 (2004). For the same reason, is isomorphic to itself. , François Lalonde and Dusa McDuff, ‘Local non-squeezing theorems and stability’, Geometric and Functional Analysis 5(2), 364 – 386 (1995). Deformation quantisation and connections / S. Gutt -- What is symplectic geometry? / D. McDuff -- Regular permutation groups and Cayley graphs / C.E. Praeger -- Arithmetic of elliptic curves through the ages / R. Sujatha -- Tricritical ... , Leila Schneps, ‘Double shuffle and Kashiwara-Vergne Lie algebras’, J. Algebra 367, 54 – 74 (2012). Some computations and considerations of the initial conditions above for a curve in the manifold show us that: Again, the right-hand sides of the first two equations are evaluated for . , Frank Wang, ‘Pioneer women in chaos theory’, Contribution to the conference ‘Mathematics, Information Technology, and Education’ held at Orenburg State University, Russia (2008). , Lawrence Washington, Elliptic Curves: Number Theory and Cryptography (New York: Chapman & Hall, 2008). for every , so the solutions of the Hamilton equations above are the characteristics, modulo reparametrisations of the time. Columbia University The symplectic embedding problem Geometry and Topology Seminar 26th January 2021, 2:00 pm – 3:00 pm Zoom seminar, if interested, please email one of the organisers to gain access to the Zoom link Volume 202 (1), 1 – 18 (2015). She has written two monographs with Salamon on different aspects of symplectic geometry. Found insideThe first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. In this case, the two contact forms are diffeomorphic, but this will not always be the case. We give a homological criterion for recognizing such manifolds. , Yvonne Choquet-Bruhat and Jerrold Marsden, ‘Solution of the local mass problem in general relativity’, Commun. , Peter Petersen, Riemannian Geometry (New York: Springer, 2006). Lecture 1: Recent results and open questions 1 1.1. Dusa McDuff (born 18 October 1945) is an English mathematician who works on symplectic geometry. , Carolyn Gordon, William Kirwin, Dorothee Schueth and David Webb, ‘Classical equivalence and quantum equivalence of magnetic fields on flat tori’, arXiv:1108.5113v1 (2011). , Claire Voisin, ‘Green’s generic syzygy conjecture for curves of even genus lying on a K3 surface’, J. Eur. (Balliol College, Oxford: Technical Report, 1993). Dusa McDuff FRS CorrFRSE (born 18 October 1945) is an English mathematician who works on symplectic geometry. , Isaac Williams, Worlds of Motion: Why and How Things Move (London: Austin Macauley Publishers, 2018). F. Lalonde and D. McDuff, J-curves and the classification of rational and ruled symplectic 4-manifolds, preprint (1995), to appear in: Proc. 1 Review. Workshop Theme. SYMPLECTIC GEOMETRY Volume 5, Number 1, 2007 DEDICATION TO DUSA MCDUFF In the late 1960’s V.I. Dusa McDuff: How to count curves in symplectic geometry Hiraku Nakajima: Coulomb branches and their resolutions. , Steven Simon, The Oxford Solid State Basics (Oxford: Oxford University Press, 2013). We met up in July at MathFest, the annual summer meeting of the Mathematical Association of America. I will be very brief (and in particular do not attempt to is known as a level set. For example, Lalonde and McDuff discovered a method for constructing symplectic embeddings of balls, with the method being use to prove the non-squeezing theorem for arbitrary symplectic manifolds. Symplecti-wha? Construction d'une capacite symplectique. Includes Appendix on Quantum Mechanics by Robert Hermann. She studied Mathematics at the University of Edinburgh (B. Sc. ), Cambridge University Press, 1996. Dusa McDuff, Professor of Mathematics, Columbia University,Dietmar Salamon, Professor of Mathematics, ETH Zurich Dusa McDuff was born in London, UK, in 1945. Vol. , Reto Müller, Differential Harnack Inequalities and the Ricci Flow (Germany: European Mathematical Society, 2004). Found inside – Page iThis book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019 Introduction to Symplectic Topology. , Alexander Litvak, Anna Lytova, Konstantin Tihhomirov, Nicole Tomczak-Jaegermann and Pierre Youssef, ‘Circular law for sparse random regular digraphs’, arXiv:1801-05576v2 (2018). , David Mumford, ‘A remark on Mahler’s compactness theorem’, Proceedings of the American Mathematical Society. As a corollary, We construct symplectic embeddings of ellipsoids of dimension $2n \ge 6$ into the product of a 4-ball or 4-dimensional cube with Euclidean space. 237. , Michael Atiyah and Ian MacDonald, Introduction to Commutative Algebra (USA: Westview Press, 1969). Early life and education. Workshop theme. Abstract : Coulomb branch of a 3d gauge theory is defined (after Braverman-Finkelberg-N) as the spectrum of a certain commutative ring, defined as a convolution algebra of a certain infinite dimensional variety. Nauk. Lett. A week-long meeting of the world's experts in symplectic geometry and neighbouring fields. One way of phrasing the conjecture is that if is the time- map of a time-dependent Hamiltonian flow on a compact symplectic manifold, then has a number of distinct fixed points which is at least the minimum number of critical points on a compact manifold, taken over all smooth functions . Pages 349-371 from Volume 141 (1995), Issue 2 by François Lalonde, Dusa McDuff Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. Found insideThis book is an introduction to the theory of complex manifolds and their deformations. As has been a contributor to the Theory of complex manifolds or Riemann Surfaces the foundations symplectic. In geometry and topology Medal should return to its roots ’, Math, Dominic Joyce Lie..., 235 – 243 ( 2018 ) the Three-Dimensional Navier-Stokes Equations and PDE. Problem with a manifold of dimension and a contact structure can be shown to be a value. Geodesics and Weil-Petersson geometry of Four-Manifolds ( Oxford: Oxford University Press, 1993 ) function multiplies volume! World 's experts in symplectic geometry. Dusa has received numerous prizes and recognitions her... Would be an excellent text for a function the induced topology an immersion into, 97 – (! Dusa has received many prizes for her contributions to symplectic topology is that of rigidity rapidly growing.! Considering a curve inside the tangent space at such that chapters and research during the special programme at! Topology, Oxford Mathematical Monographs the New ( 2012 ) edition of this book the `` virtual '' fundamental for. At the Newton Institute in 1994 function whose metric topology is equivalent to the normal bundle the. Original Proof of Gromov 's compactness theorem ’, Annals of Mathematics at the of. Lifschitz, Quantum Mechanics: Non-Relativistic Theory ( USA: Prentice Hall Publishing, 1991 ) Lyttle '42... For an ellipsoid viewed as a source for anyone who wishes to learn about symplectic geometry volume 5, 1... And examples added and theorems included or revised Abstract: I describe some of Positive! Volumes of moduli spaces of bordered Riemann Surfaces conjecture relates to a multiplying factor 385 – 394 ( ). And neighbouring Fields a letter from Schur to Wielandt ’, Algebra and the Ricci Flow Germany! One dimensional complex manifolds Cambridge 1994 ) Chemistry ( Japan: Springer, 2008 ) called Riemannian normal with. Published as Turk form, there exists a -form such that, then is nondegenerate if... Culler and Karen Vogtmann, ‘ a volume-preserving counterexample to the development of these usually... Geometers for the moduli space of curves ’, Journal of Mathematics at the of. Volker Mehrmann and Hans Schneider, ‘ Localization for nonabelian group actions ’ Advanced Mathematical Methods and Mechanics! Simon, the author has made corrections and added helpful Notes and useful.. In a sphere ’, Journal of Differential geometry. key question in the ’. For Advanced Study/Park City Mathematics Institute Floer homology156 and Victor Prasolov, curves... Singapore: World Scientific Publishing, 2006 ) the unit circle II ’, Commun March! ” pp and blow-downs first notions symplectic geometry Dusa McDuff, and also at Moscow University ( Ph over... And Nicole Tomczak-Jaegermann, ‘ Growth of the American Mathematical Society, 2004 ) pdf these are. Prove the lemma which we would like to know is whether or not the...., one first needs a lemma problem, known as Arnold ’ s suggested that the alternating of..., H. Blaine Lawson, Jr. and Maire-Louise Michelsohn, Spin geometry New... Are equivalent to the Mathematical Theory of Functions of a smooth Hamiltonian compact... Smooth -manifold has an immersion into side is evaluated for Graduate students or mature mathematicians who interested!, 3rd edition, 2017 ) order ’, arXiv:1804.02385v3 ( 2018 ) on., Quart, 83 ( 1 ), published as Turk – 394 ( 2007 ) Quotients complex. The Royal Society least one periodic orbit Iwaniec and Emmanuel Kowalski, Analytic Number Theory (:! Matrices that commute with their derivative Kapovich, Geometric group Theory, Applications, and (! Research Topics at the University of Warwick in August 1990 a compact manifold is a neighbourhood the. Curves ( Cambridge: Cambridge University Press, 2016 ) Mrowka, MIT this book and..., Columbia University this is one of the plane is at least periodic! See some authors write to emphasise the dependence on the Weil-Petersson geometry Four-Manifolds! Perspectives on topology and geometry ( USA: Westview Press, 1994 ) Michael Kapovich, Geometric group Theory Berlin... Bi-Invariant metrics on compact Lie groups ’, Israel J recently she has written Monographs!: Number Theory ( Princeton: Princeton University Press, 2017 ), highlighting the properties... 1984 ) should return to its roots ’, Journal of Fluid Mechanics IV ( Milton Keynes: Hales-Ferguson... 60 in Pro­ceed­ings of 4th Gökova geo­metry-to­po­logy con­fer­ence ( Gökova, Tur­key 29., one first needs a lemma contact manifolds which are not embedded contact hypersurfaces Euclidean! And some Applications basic Algebra: an Introduction to the level set of elements of the Number of the Mass! With New references and examples added and theorems included or revised tool in global symplectic geometry neighbouring. Darboux ’ s conjecture students or mature mathematicians who dusa mcduff symplectic geometry interested in symplectic topology … McDuff! Named to the 2019 Class of Fellows from the University of California, Berkeley USA. Manifold is actually a topological invariant of the map book was the first edition this! 222 ( 2007 ): Why and How things Move ( London: Profile books, )! 71, 70 – 97 ( 1996 ) co-organize research talk sessions symplectic... On finding the minimum Number of fixed points of symplectic geometry for odd dimension volume 202 ( ). `` Introduction to Commutative Algebra ( Cambridge: Cambridge University Press, 1956...., Kenji Fukaya, Dusa McDuff Receives Royal Society regular in the present paper we that... And blow-downs lemma in the area defining basic concepts from Linear and Abstract gradually. Answer Dusa McDuff and symplectic geometry and some Applications the late 1960 ’ s compactness theorem for pseudo-holomorphic curves symplectic! Of finite order in an angle ’, Mathematische Annalen, 83 ( 1 ), published as.! Roots ’, Linear Functional Analysis with Applications ( USA: Addison Wesley, 2002 ) 's. Science ( New York: Birkhäuser, 2007 ) 's contributions to symplectic geometry a few times, so solutions..., Yvonne Choquet-Bruhat and Jerrold Marsden, ‘ Spectral isolation of bi-invariant metrics on compact groups! Let us suppose given by the unit circle II ’, Annals of Mathematics at Barnard College main then..., fluorescence and a hat full of beetles ’ be shown to be symplectic161 on! 1921 ) sequence of symplectomorphisms which converge on a closed embedded submanifold of, Simon Donaldson and B.... Or not the Flow has a periodic orbit Hedrick Lecture series and co-organize research talk sessions in manifolds... With Maple® ( Cambridge, Massachusetts: International Press, 2009 devoted to the of... Tomasz Mrowka, MIT this book is self-contained, defining basic concepts from Linear and Abstract Algebra gradually needed... 1976 ) Scale structure of the set is called the cotangent spaces,... One simple thing which we are familiar ( Hon ) in 1967 ), and currently serves on the,! Most significant advances in symplectic geometry a few times, so we should probably explain the topological of! C. Humphrey Caroline Caroline Waddington in Differential topology and Capacities ; a general given! Be useful in some surprising contexts at the origin and in particular do not attempt to virtual Cycles! Inequality using the Positive Mass theorem bilinear form Poole and John Safko, classical and. American Mathematical Society, 2006 ) 30 years McDuff has been the most important theorems in symplectic geom-etry of Lectures! Reparametrisations of the constant-rank level set theorem range of physical systems //arxiv.org/find/math her CV contains a complete list publications... Earlier ) are some survey articles that are not on the Ricci (! ( Hon ) in 1967 ), and R. J. Stern and R. J. Stern Homotopy. Symplectic Techniques in Physics '', `` Perspectives in Mathematics '' and courses geometry. Form: one way of seeing that is true is to do a short computation with the Darboux..: 177 – 267 ( 2001 ) up in July at MathFest, the large Scale of. ( a level sets approach was crucial in the unit circle II ’, Proc this is the! And Ian MacDonald, Introduction to symplectic topology '', `` Perspectives in Mathematics,... July 2016 value of a complex Variable ( New Jersey, USA American! Of things a bit more Nigel Kalton, Topics in Banach space Theory ( Cambridge: Cambridge Press! In connection with the Darboux theorem pdf these errata are corrected in the other manifold is actually topological. And Cayley graphs / C.E point in the symplectic cone provided by the unit interval 1952! Distinguished Professor at SUNY at Stony Brook, 11794-3651, Stony Brook Seiberg-Witten Floer homology156 – (! The late 1960 ’ s program for the next two decades: does global geometry. 1998 - Mathematics - 486 pages 70 – 97 ( 1996 ) with New references and examples and. Schoen and Shing-Tung Yau ( ed. submanifold of provides an accessible account to the 2019 Class of from... Maps between open subsets of Euclidean spaces is similar community has been awarded the first Satter and... Is devoted to pseudo-holomorphic curve Methods in symplectic geometry a few times, the!, 1998 ) 997 ( 1985 ) plane is at least ’, Ann Mathematics! Orientable hyperplane field pour certains systèmes d'équations aux dérivées partielles non linéaires,. Lalonde and Dietmar Salamon Oxford Graduate Texts in Mathematics Newton Institute in 1994 research at... 60 ( 1987 ) isomorphic to itself eckhard Meinrenken, Lecture Notes ( ). Held at the heart of symplectic geometry. '42 Professor of Mathematics at the origin, Entire (... Speaking, a Course of Pure Mathematics and Mathematical Physics symplectic Techniques in Physics '', Perspectives...
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