He was an invited speaker at international congress of mathematicians, beijing2002. Hard lefschetz property of symplectic structures on compact kaehler manifolds. Eckhard meinrenken based on work with alejandro cabrera and. Home page of eckhard meinrenken department of mathematics. A symplectic form on a smooth manifold mis a smooth closed, nondegenerate 2form. Clifford algebras and lie groups eckhard meinrenken. This distinguishes it from riemannian geometry, where curvature obstructs isometric identi cation of small patches on di erent manifolds. Fellowship of the royal society of canada since 2008, steacie fellowship 2007, mclean award 2003, andre aisenstadt prize 2001. Another important instance is the theory of integrable. These notes approximately transcribe a 15week course on symplectic geometry i taught at uc berkeley in the fall of 1997. Among the regular participants in the mit informal symplectic seminar 9396, i would like to acknowledge the contributions of allen knutson, chris woodward, david metzler, eckhard meinrenken, elisa prato, eugene.
Generalized geometry is a recent approach to geometric structures with the ability of uniting, for instance, complex and symplectic geometry. Symplectic geometr y of pol ygons in 3sphere thomas trelo ar y abstra ct. Symplectic geometry seminar, quantization of the linear symplectic. Symplectic structuresa new approach to geometry pdf. W e pro v that these mo duli spaces ha v e symplectic structures obtained b y reduction of the fusion pro duct n conjugacy classes in s u 2, denoted c n r, b y the diagonal conjugation action of 2. Introduction to differential geometry lecture notes download book. W e study the symplectic geometry of mo duli spaces m r s 3 closed ngons with xed sidelengths in the 3sphere. Eckhard meinrenken submitted on 16 sep 2002 v1, last revised 14 jul 2003 this version, v3. Industry applications educationlearning, research research interests symplectic geometry, mathematical physics, lie theory education albertludwig universitaet. Riemannian geometry eckhard meinrenken lecture notes, university of toronto, spring. Symplectic geometry eckhard meinrenken lecture notes, university of toronto spring 2000 projective di fferential geometry old and new. In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold. Eckhard meinrenken toronto tom baird, university of toronto, toronto, ontario, m5s 2e4, canada.
Professor university of toronto, department of mathematics. The goal of this project has been to compare two different viewpoints symplectic and algebraic and i owe a lot to friedrich knop for patiently explaining the algebraic perspective and contributing many important ideas. Linear transformations, tangent vectors, the pushforward and the jacobian, differential oneforms and metric tensors, the pullback and isometries, hypersurfaces, flows, invariants and the. Hypothesis for the main results changed from 2large to 3large, added sections 3. Download introduction to differential geometry lecture notes download free online book chm pdf. Copyright 2015 department of mathematics, university of toronto room 6290, 40 st. Eckhard meinrenken, clifford algebras and lie theory find, read and cite all the research you need on researchgate. In this paper, we solve the problem of giving a gaugetheoretic description of the natural dirac structure on a lie group which plays a prominent role in the theory of d branes for the wesszuminowitten model as well as the theory of quasi. A pdf version of the schedule can also be downloaded here. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
Introduction to differential geometry lecture notes. The book starts with a detailed presentation of the main results on symmetric bilinear forms and clifford algebras. Eckhard meinrenken, symplectic surgery and the spin c spincdirac operator, adv. The course at berkeley was greatly inspired in content and style by victor guillemin, whose masterly teaching of beautiful courses on topics related to s plectic geometry at mit, i was lucky enough to experience as a graduate student. Poisson geometry university of toronto math department. Eckhard meinrenken submitted on 26 apr 1995 v1, last revised 30 dec 1996 this version, v4. Nicole berline, michele vergne, hamiltonian manifolds and moment maps pdf. To specify the trajectory of the object, one requires both the position q and the momentum p, which form a point p, q in the euclidean plane. Eckhard meinrenken professor expert with university of. In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, m \displaystyle m, equipped with a closed nondegenerate differential 2form. By anton alekseev, eckhard meinrenken and chris woodward download pdf 336 kb abstract. David libland, eckhard meinrenken, courant algebroids and poisson geometry, in international mathematics research notices, no. Reyer sjamaar, symplectic reduction and riemannroch formulas for multiplicities, bull. A celebration of symplectic geometry for more information visit the website.
He is a professor at the university of toronto department of mathematics he was an invited speaker at international congress of mathematicians, beijing2002 honors. Hans duistermaat, an influential geometeranalyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple lie groups, mechanics, mathematical physics, and related fields. Eckhard meinrenken, university of toronto ana rita pires, fordham university. Many concepts, like diffeomorphism or metric, have their generalized counterpart, some of which have found an application within mathematics or theoretical physics.
W e pro v that these mo duli spaces ha v e symplectic structures obtained b y reduction of the fusion pro duct n conjugacy classes in s u 2, denoted c n. In 2006 he, with eckhard meinrenken, published in inventiones mathematicae a proof of the kashiwaravergne conjecture. There are several books on symplectic geometry, but i still took the trouble of writing up lecture notes. Microlocal geometry, in a rough sense, provides is with analytic objects that arise as solutions to a very broad class of operator equations. By work of atiyah, bott, duistermaat, guillemin, sternberg and many others at the beginning of the 80s, hamiltonian group actions. Lietheoretic techniques inform much of the modern research conducted in symplectic and poisson geometry. Courses publications lecture notes symplectic seminar. Our main sources have been the books symplectic techniques by guilleminsternberg and introduction to symplectic topology by mcdu. Lectures on symplectic geometry pdf 225p this note contains on the following subtopics of symplectic geometry, symplectic manifolds, symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, kahler manifolds, hamiltonian mechanics, moment maps, symplectic reduction, moment maps revisited and symplectic toric.
Clifford algebras and lie theory eckhard meinrenken springer. Talks mca2017 symmetries of symplectic manifolds and. A suggestion that geometric pushforward quantization is best understood to proceed to take values in kktheory is in. Deformation spaces and normal forms around transversals. Symplectic geometry, mathematical physics, lie theory.
By eugene lerman, eckhard meinrenken, sue tolman and chris woodward abstract in this paper we extend the results of kirwan et alii on convexity properties of the moment map for hamiltonian group actions, and on the connectedness of the fibers of the moment map, to the case of noncompact orbifolds. Eckhard meinrenken, professor department of mathematics university of toronto 40 st. On the geometric quantization of some poisson manifolds 10. Symplectic geometry arose from the study of classical mechanics and an example of a symplectic structure is the motion of an object in one dimension. Eckhard meinrenken, lectures on groupvalued moment maps and. Symmetries of symplectic manifolds and related topics. Mosers lemma and local triviality of symplectic differential geometry 17 2. We prove a multiplicity formula for riemannroch numbers of reductions of hamiltonian actions of loop groups. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent. Our main sources have been the books symplectic techniques by guilleminsternberg and introduction to symplectic topology by mcduffsalamon, and the paper stratified symplectic spaces and. Eckhard meinrenken view email v1 wed, 26 apr 1995 22. Alejandro cabrera, marco gualtieri, eckhard meinrenken submitted on 25 aug 2015 abstract. This monograph provides an introduction to the theory of clifford algebras, with an emphasis on its connections with the theory of lie groups and lie algebras.
Symplectic surgery and the spinc dirac operator authors. Symplectic geometry is a branch of differential geometry studying symplectic manifolds and some generalizations. Main areas of research are symplectic geometry, with applications to lie theory and mathematical physics. From linear algebra to the nonsqueezing theorem of symplectic. Hans duistermaat, victor guillemin, eckhard meinrenken, siye wu, symplectic reduction and riemannroch for circle actions. The goal of this project has been to compare two different viewpoints symplectic and algebraic and i owe a lot to friedrich knop for patiently explaining. Eckhard meinrenken professor at university of toronto, department of mathematics toronto, on, ca eckhard meinrenken researches symplectic geometry, mathematical physics, and lie theory. An introduction to symplectic topology through sheaf theory. Holomorphic curves in symplectic and contact geometry work in progressversion 3. Multiplicityfree hamiltonian actions and existence of. Fixed gap in first version the proof of corollary 3. If m is poisson, h m a principal action by poisson automorphisms, then mh is poisson. Rita, mundet i riera, ignasi, and salamon, dietmar a. Lerman, jonathan weitsman, lisa jeffrey, reyer sjamaar, shaun martin.
Eckhard meinrenken university of toronto canada leonardo mihalcea virginia tech usa. Symmetries of symplectic manifolds and related topics a special session in the mathematical congress of the americas 2017 montreal, canada july 24 28, 2017 home talks schedule objective. Bypass attachments in higherdimensional contact topology. Applications of algebraic microlocal analysis in symplectic. The reason is that this one semester course was aiming for students at the beginning of their masters. Manifolds, oriented manifolds, compact subsets, smooth maps, smooth functions on manifolds, the tangent bundle, tangent spaces, vector field, differential forms, topology of manifolds, vector bundles. He is a professor at the university of toronto department of mathematics. Among the regular participants in the mit informal symplectic seminar 9396, i would like to acknowledge the contributions of allen knutson, chris woodward, david metzler, eckhard meinrenken, elisa prato. That course also borrowed from the 1997 park city summer courses on symplectic geometry and topology, and from many talks and discussions of the symplectic geometry group at mit. Fall 2017 math 70330 \intermediate geometry and topology pavel mnev detailed plan. Nonabelian convexuty by symplictic cuts new jersey.
The study of symplectic manifolds is called symplectic geometry or symplectic topology. Momentum maps in higher geometry, higher geometric prequantum theory, are. Other readers will always be interested in your opinion of the books youve read. Equivariant perfection and kirwan surjectivity in real symplectic geometry abstract. The basic gerbe over a compact simple lie group authors. Lie groups and lie algebras eckhard meinrenken lecture notes, university of toronto, fall symplectic geometry eckhard meinrenken lecture notes, university of toronto spring 2000. Symmetries of symplectic manifolds and related topics a special session in the mathematical congress of the americas 2017. This theorem not only recovers the global construction of symplectic realizations from crainic and marcut j symplectic geom 94. These are lecture notes for a course on symplectic geometry in the dutch mastermath program.
In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, equipped with a closed nondegenerate differential 2form, called the symplectic form. In 1999, fuchs and schweigert proposed formulas of verlinde type for moduli spaces of surface group representations in compact nonsimply connected lie groups. The ones by cannas da silva are the easiest to manage with less mathematical background. Free differential geometry books download ebooks online. David metzler, a ktheoretic note on geometric quantization arxiv. Darbouxs theorem is frequently interpreted as saying that symplectic geometry has \no local invariants. Symplectic geometry eckhard meinrenken lecture notes, university of toronto these are lecture notes for two courses, taught at the university of toronto in spring 1998 and in fall 2000.
Clifford algebras and lie theory eckhard meinrenken. There are three sets of notes on symplectic geometry that i nd useful, each with its individual avor. The symplectic vortex equations and invariants of hamiltonian group actions cieliebak, kai, gaio, a. In this paper, we will prove a symplectic version of their conjecture for surfaces with at most one boundary component. Symplectic geometry is a geometry of even dimensional spaces in which area measurements. Eckhard meinrenken frsc is a canadian mathematician specializing in symplectic geometry, lie theory, mathematical physics.