The reason is that this one semester course was aiming for students at the beginning of their masters. Clifford algebras and lie theory eckhard meinrenken springer. Symplectic surgery and the spinc dirac operator authors. 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, symplectic surgery and the spin c spincdirac operator, adv. Generalized geometry is a recent approach to geometric structures with the ability of uniting, for instance, complex and symplectic geometry. Fixed gap in first version the proof of corollary 3. Hypothesis for the main results changed from 2large to 3large, added sections 3. Industry applications educationlearning, research research interests symplectic geometry, mathematical physics, lie theory education albertludwig universitaet. These are lecture notes for two courses, taught at the university of. Holomorphic curves in symplectic and contact geometry work in progressversion 3. W e study the symplectic geometry of mo duli spaces m r s 3 closed ngons with xed sidelengths in the 3sphere.
Free differential geometry books download ebooks online. 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. 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. Deformation spaces and normal forms around transversals. Linear transformations, tangent vectors, the pushforward and the jacobian, differential oneforms and metric tensors, the pullback and isometries, hypersurfaces, flows, invariants and the. He was an invited speaker at international congress of mathematicians, beijing2002. By anton alekseev, eckhard meinrenken and chris woodward download pdf 336 kb abstract. 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. A pdf version of the schedule can also be downloaded here. Fellowship of the royal society of canada since 2008, steacie fellowship 2007, mclean award 2003, andre aisenstadt prize 2001.
Equivariant perfection and kirwan surjectivity in real symplectic geometry abstract. We explain a construction of an lgequivariant spinor module over any hamiltonian loop group space with proper moment map. Lectures on symplectic geometry by cannas da silva, ana. 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. On the geometric quantization of some poisson manifolds 10. He is a professor at the university of toronto department of mathematics he was an invited speaker at international congress of mathematicians, beijing2002 honors. 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. In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, m \displaystyle m, equipped with a closed nondegenerate differential 2form. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent. Eckhard meinrenken submitted on 16 sep 2002 v1, last revised 14 jul 2003 this version, v3.
Applications of algebraic microlocal analysis in symplectic. 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. Alekseev does research on representation theory of lie groups and algebras, moment theory, symplectic geometry and mathematical physics. From linear algebra to the nonsqueezing theorem of symplectic. There are several books on symplectic geometry, but i still took the trouble of writing up lecture notes. He is a professor at the university of toronto department of mathematics. Symplectic geometry eckhard meinrenken lecture notes, university of toronto spring 2000 projective di fferential geometry old and new. Microlocal geometry, in a rough sense, provides is with analytic objects that arise as solutions to a very broad class of operator equations. 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.
Eckhard meinrenken frsc is a canadian mathematician specializing in symplectic geometry, lie theory, mathematical physics. Nonabelian convexuty by symplictic cuts new jersey. The symplectic vortex equations and invariants of hamiltonian group actions cieliebak, kai, gaio, a. Multiplicityfree hamiltonian actions and existence of. In this paper, we will prove a symplectic version of their conjecture for surfaces with at most one boundary component.
The basic gerbe over a compact simple lie group authors. Introduction to differential geometry lecture notes. The ones by cannas da silva are the easiest to manage with less mathematical background. A symplectic form on a smooth manifold mis a smooth closed, nondegenerate 2form. Symplectic geometry is a geometry of even dimensional spaces in which area measurements. Symplectic geometry is a branch of differential geometry studying symplectic manifolds and some generalizations. Eckhard meinrenken view email v1 wed, 26 apr 1995 22. 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. Home page of eckhard meinrenken department of mathematics. Clifford algebras and lie theory eckhard meinrenken. Many concepts, like diffeomorphism or metric, have their generalized counterpart, some of which have found an application within mathematics or theoretical physics. Momentum maps in higher geometry, higher geometric prequantum theory, are.
There are three sets of notes on symplectic geometry that i nd useful, each with its individual avor. Professor university of toronto, department of mathematics. Other readers will always be interested in your opinion of the books youve read. These are lecture notes for a course on symplectic geometry in the dutch mastermath program. Symplectic geometry seminar, quantization of the linear symplectic. Eckhard meinrenken, professor department of mathematics university of toronto 40 st. An introduction to differential geometry through computation. 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. Another important instance is the theory of integrable. 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. 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. 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. Symmetries of symplectic manifolds and related topics a special session in the mathematical congress of the americas 2017.
Main areas of research are symplectic geometry, with applications to lie theory and mathematical physics. Eckhard meinrenken professor at university of toronto, department of mathematics toronto, on, ca eckhard meinrenken researches symplectic geometry, mathematical physics, and lie theory. Eckhard meinrenken, clifford algebras and lie theory find, read and cite all the research you need on researchgate. Poisson geometry university of toronto math department. Eckhard meinrenken based on work with alejandro cabrera and. In 2006 he, with eckhard meinrenken, published in inventiones mathematicae a proof of the kashiwaravergne conjecture. Fall 2017 math 70330 \intermediate geometry and topology pavel mnev detailed plan. Eckhard meinrenken university of toronto april 16 april 21, 2017 1 overview groups typically arise as the symmetries of some given object. If m is poisson, h m a principal action by poisson automorphisms, then mh is poisson. Hans duistermaat, victor guillemin, eckhard meinrenken, siye wu, symplectic reduction and riemannroch for circle actions. Download introduction to differential geometry lecture notes download free online book chm pdf.
Darbouxs theorem is frequently interpreted as saying that symplectic geometry has \no local invariants. In 1999, fuchs and schweigert proposed formulas of verlinde type for moduli spaces of surface group representations in compact nonsimply connected lie groups. Nicole berline, michele vergne, hamiltonian manifolds and moment maps pdf. By work of atiyah, bott, duistermaat, guillemin, sternberg and many others at the beginning of the 80s, hamiltonian group actions. Eckhard meinrenken, university of toronto ana rita pires, fordham university. 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. Lerman, jonathan weitsman, lisa jeffrey, reyer sjamaar, shaun martin. We determine symplectic leaves on the grothendieck resolution, and show.
Lie groups and lie algebras eckhard meinrenken lecture notes, university of toronto, fall symplectic geometry eckhard meinrenken lecture notes, university of toronto spring 2000. This distinguishes it from riemannian geometry, where curvature obstructs isometric identi cation of small patches on di erent manifolds. Courses publications lecture notes symplectic seminar. Eckhard meinrenken, lectures on groupvalued moment maps and. 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. 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. A celebration of symplectic geometry for more information visit the website. Symplectic geometry, mathematical physics, lie theory. These notes approximately transcribe a 15week course on symplectic geometry i taught at uc berkeley in the fall of 1997.
Geometric aspects of analysis and mechanics springerlink. Mosers lemma and local triviality of symplectic differential geometry 17 2. Bypass attachments in higherdimensional contact topology. Eckhard meinrenken toronto tom baird, university of toronto, toronto, ontario, m5s 2e4, canada.
David metzler, a ktheoretic note on geometric quantization arxiv. Talks mca2017 symmetries of symplectic manifolds and. 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. 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. This theorem not only recovers the global construction of symplectic realizations from crainic and marcut j symplectic geom 94. Symplectic geometr y of pol ygons in 3sphere thomas trelo ar y abstra ct. Alejandro cabrera, marco gualtieri, eckhard meinrenken submitted on 25 aug 2015 abstract. Riemannian geometry eckhard meinrenken lecture notes, university of toronto, spring. Eckhard meinrenken professor expert with university of. We prove a multiplicity formula for riemannroch numbers of reductions of hamiltonian actions of loop groups. Our main sources have been the books symplectic techniques by guilleminsternberg and introduction to symplectic topology by mcdu. Copyright 2015 department of mathematics, university of toronto room 6290, 40 st. Hard lefschetz property of symplectic structures on compact kaehler manifolds. Eckhard meinrenken university of toronto canada leonardo mihalcea virginia tech usa.
A suggestion that geometric pushforward quantization is best understood to proceed to take values in kktheory is in. 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. Lietheoretic techniques inform much of the modern research conducted in symplectic and poisson geometry. Home page of eckhard meinrenken university of toronto. Deformation spaces and normal forms around transversals volume 156 issue 4 francis bischoff, henrique bursztyn, hudson lima, eckhard meinrenken skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. The book starts with a detailed presentation of the main results on symmetric bilinear forms and clifford algebras. 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.
Symmetries of symplectic manifolds and related topics. Introduction to differential geometry lecture notes download book. Clifford algebras and lie groups eckhard meinrenken. Symplectic structuresa new approach to geometry pdf.
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