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Topic: Symplectic geometry

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	PlanetMath: Darboux's Theorem (symplectic geometry)
		Darboux's theorem implies that there are no local invariants in symplectic geometry, unlike in Riemannian geometry, where there is curvature.
		Cross-references: curvature, geometry, invariants, implies, symplectomorphism, symplectic form, pullback, canonical, coordinate chart, neighborhood, symplectic manifold
		This is version 2 of Darboux's Theorem (symplectic geometry), born on 2002-12-12, modified 2005-05-09.
	planetmath.org /encyclopedia/DarbouxsTheoremSymplecticGeometry.html (76 words)

	Journal of Symplectic Geometry, Volume 4, no. 1
		The Journal of Symplectic Geometry is a new journal focusing on the impact of symplectic geometry in mathematics.
		Symplectic geometry has deep roots in mathematics going back to Huygens' study of optics and the Hamilton Jacobi formulation of mechanics.
		The symplectic geometry of the Gel'fand--Cetlin--Molev basis for representations of $Sp(2n,\C)$
	projecteuclid.org /Dienst/UI/1.0/Journal?authority=euclid.jsg (68 words)

	Symplectic topology - Wikipedia, the free encyclopedia
		Symplectic topology (also called symplectic geometry although the terms are not completely synonymous) is a branch of differential topology/geometry which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form.
		Symplectic topology has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.
		Symplectic topology has a number of similarities and differences with Riemannian geometry, which is the study of differentiable manifolds equipped with nondegenerate, symmetric 2-tensors (called metric tensors).
	en.wikipedia.org /wiki/Symplectic_geometry (338 words)

	UCSC Mathematics Research
		Symplectic geometry is the geometry underlying classical mechanics and is important to quantum mechanics and low-dimensional topology, and is an active area of research.
		Her work is an interplay between group theory, symplectic geometry, and uses a good deal of symbolic manipulation.
		Riemannian or pseudo-Riemannian (general relativistic) geometry on one manifold to the conformal geometry of a manifold which bounds it.
	www.math.ucsc.edu /research/index.html (911 words)

	Contact geometry - Wikipedia, the free encyclopedia
		One difference between contact and symplectic geometry is that every 3-manifold admits a contact structure while there are cohomological obstructions to the existence of symplectic structures.
		Contact geometry also has applications to low-dimensional topology; for example, it has been used by Kronheimer and Mrowka to prove the property P conjecture and by Gompf to derive a topological characterization of Stein manifolds.
		Legendrian submanifolds are analogous to Lagrangian submanifolds of symplectic manifolds.
	en.wikipedia.org /wiki/Contact_geometry (768 words)

	CJM - The Symplectic Geometry of Polygons in the 3-Sphere
		CJM - The Symplectic Geometry of Polygons in the 3-Sphere
		The Symplectic Geometry of Polygons in the 3-Sphere
		We study the symplectic geometry of the moduli spaces $M_r=M_r(\s^3)$ of closed $n$-gons with fixed side-lengths in the $3$-sphere.
	journals.cms.math.ca /cgi-bin/vault/view/0treloar1378 (179 words)

	Contact and Symplectic Geometry - Cambridge University Press
		Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention.
		Introduction to symplectic Floer homology Matthias Schwarz; 9.
		Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds Yong-Geun Oh; 11.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521570867 (371 words)

	Symplectic Geometry Seminar
		This is the satellite conference of the ICM 2006, Madrid, in the field of global differential geometry.
		The purpose of the conference is to highlight the interactions of group theory with topology and geometry.
		Geometry Conference in honour of Nigel Hitchin, on the occasion of his 60th birthday, September 4--8, 2006.
	www.math.toronto.edu /symplec/announce.html (785 words)

	Stanford Symplectic Geometry Seminar 2004-2005
		Abstract: We shall discuss an existence theorem for foliated bundles with symplectic total holonomy, and its relationship to the homology of symplectomorphism groups.
		It turns out that the corresponding results in contact geometry exhibit a quantum behavior: there are non-squeezing results for domain of size larger than $\hbar$ but not for small ones.
		In this talk, we will explain how to use symplectic geometry to understand their deformation and various related structures.
	math.stanford.edu /~lipshitz/seminar0405 (2052 words)

	Symplectic geometry (L24) (Site not responding. Last check: 2007-10-19)
		Originally motivated by classical mechanics and dynamics, symplectic geometry also plays a key role in low-dimensional topology, in algebraic geometry and in theoretical physics (both in gauge theory and in various aspects of string theory, notably mirror symmetry).
		This course shall cover a wide swathe of the basic theory of symplectic manifolds, later concentrating on Gromov's theory of pseudoholomorphic curves - a showcase example of how to define topological invariants using infinite-dimensional analysis.
		Examples of symplectic manifolds: Kähler manifolds, blow-ups and symplectic sums, reduction.
	www.maths.cam.ac.uk /CASM/courses/02-03/descriptions/node23.html (170 words)

	SYMPOSIUM ON SYMPLECTIC GEOMETRY 1997--2000, REPORT
		The mathematical topics covered a wide range of subjects centered around symplectic topology and geometry, as well as its many applications and related areas such as Kähler and algebraic geometry or the use of symmetry in mechanics, and several joint activities with these groups were organised (programmes are appended).
		Symplectic geometry also featured prominently in presentations by Eugene Lerman (Illinois) and Mark Roberts (Warwick), both of whom described recent results on bifurcations of relative equilibria.
		Their proof involves the study of symplectic fibrations over the 2-sphere, and is based on the work of Seidel [128].
	www.maths.warwick.ac.uk /mrc/1997-98/report.html (8037 words)

	Recent Developments in Symplectic Geometry (Site not responding. Last check: 2007-10-19)
		This will be a survey for nonexperts of the circle of ideas considered in modern symplectic topology.
		They are mostly based on studying the properties of the holomorphic curves in a symplectic manifold.
		Finally I will discuss some of the new insights from string theory that shed light on classical problems of enumerative geometry, such as how to count the number of rational curves in the complex plane.
	www.math.temple.edu /events/grosswald/abstractmcduff.html (124 words)

	Penn State Symplectic Geometry Workshop
		Title: Groups of symplectic diffeomorphisms and the topology of the space of symplectic embeddings of the standard ball in rational 4-manifolds.
		Abstract: Let $M_{\mu}$ be the rational $4$-manifold $S^2 \times S^2$ equipped with the normalised symplectic form $\omega_{\mu} = \omega(\mu) \oplus \omega(1)$ that gives the area $\mu \ge 1$ to the first factor and area $1$ to the second.
		We compute the rational homotopy type of the space $Emb(r, \mu)$ of all symplectic embeddings of the standard ball of radius $r$ in $M_{\mu}$.
	www.math.psu.edu /cgmp/conferenceabstracts.htm (634 words)

	Mathematics Geometry
		The Geometry Group at UCSB concentrates on relationships between curvature and topology of Riemannian manifolds and global analysis techniques for studying many problems in Riemannian and symplectic geometry.
		One of the reasons this theorem is important is that it unifies many branches of mathematics, differential geometry, partial differential equations, and topology.
		The Atiyah-Singer theorem is now used as one of the basic tools in studying nonlinear PDE's that arise is geometry, including the equations for pseudoholomorphic curves which revolutionized symplectic geometry, and the Seiberg-Witten equations which revolutionized four-dimensional topology a few years ago.
	www.math.ucsb.edu /department/geometry.php (267 words)

	University of Michigan Department of Mathematics: Symplectic Geometry and Hamiltonian Mechanics
		The permanent faculty members who specialize in Symplectic Geometry and Hamiltonian Mechanics are Anthony Bloch, Dan Burns, Alejandro Uribe, Michael Weinstein.
		Symplectic geometry and Hamiltonian dynamics spans from the core areas of symplectic topology to applied areas such as control theory and robotics.
		This area has seen tremendous growth in the last decade, due to new ground-breaking foundational work on the topology of symplectic manifolds, better understanding of their symmetries and new applications in physics and engineering.
	www.math.lsa.umich.edu /~fornaess/symplectic.html (360 words)

	ARCC Workshop: Holomorphic curves in contact geometry (Site not responding. Last check: 2007-10-19)
		This workshop, sponsored by AIM and the NSF, will be devoted to the development of holomorphic curve techniques in contact geometry and topology.
		The advent of holomorphic curve techniques in contact topology, as exemplified in Symplectic Field Theory (SFT), and asymptotically holomorphic curve techniques, in the spirit of Donaldson, has allowed one to use a diverse set of geometric, analytic and topological tools when studying contact structures.
		The workshop will bring together researchers in contact and symplectic geometry, dynamics, low-dimensional topology and physics, who will explore connections between the various approaches people have taken to using holomorphic curves, develop new holomorphic curve techniques and apply them to various questions in contact and symplectic geometry and low-dimensional topology.
	www.aimath.org /ARCC/workshops/contactgeom2.html (325 words)

	Stanford Symplectic Geometry Seminar 2006-2007
		The basic idea of non-commutative geometry is to construct the convolution algebra of the groupoid representing the stack, which yields the non-commutative torus algebra, and study it as if it were the algebra of functions on the quotient.
		Tori and such surfaces are particular examples of the so-called symplectically aspherical manifolds, as are all symplectic manifolds with zero second homotopy group.
		Of course, one can expect the Conley conjecture to be true for a general closed symplectically aspherical manifold and numerous partial results to this effect have been proved in the context of symplectic topology.
	math.stanford.edu /~erics/seminar0607 (1775 words)

	Math 242: Symplectic Geometry, Fall '00
		I will emphasize symplectic geometry from the Kahler geometry (rather than Poisson) viewpoint, and most of my examples will be from the algebraic-geometry world.
		While symplectic techniques are proving useful in 4-manifold theory, I will instead be thinking of them as nice places to see Lie groups act (no prior knowledge of Lie groups will be assumed, however).
		This is NOT to be confused with "deformation quantization", which deforms the symplectic manifold to a noncommutative space (and is the study of Math 277 this term).
	math.berkeley.edu /~allenk/courses/fall00/242 (927 words)

	Symplectic geometry (Site not responding. Last check: 2007-10-19)
		of a symplec manifold known as symplectic capacity.
		Finally we embark on the construction of a particular symplectic capacity due to Hofer and Zehnder, 1990.
		This involves a number of ideas from global analysis to be introduced in the course.
	www.imf.au.dk /da/uddannelse/beskrivelser/older/F2000/node25.html (131 words)

	Geometry at Imperial
		The geometry group at Imperial carries out research in several areas, ranging through differential and algebraic geometry and geometric group theory.
		The Geometry and Topology seminar, held jointly with King's College and Queen Mary's.
		The COW seminar, on algebraic geometry, held jointly with Cambridge, Oxford and Warwick.
	www.ma.ic.ac.uk /geometry (261 words)

	Symplectic Geometry - Fall 2004 (Site not responding. Last check: 2007-10-19)
		Symplectic Manifolds - in PDF or PostScript (posted Sept. 20)
		Symplectic Geography - to be posted as soon as possible
		Symplectic Reduction - in PDF or PostScript (posted Dec. 5)
	www.math.princeton.edu /~acannas/04_SG (131 words)

	Symplectic geometry
		The first series will give the basic theory of holomorphic symplectic geometry in an algebro-geometric setting.
		A synopsis, with references to reading material of these lectures are available in pdf format.
		The second one will treat Riemannian holonomy groups and calibrated geometry with a main focus on Kahler geometry and Calabi-Yau manifolds as well as special Lagrangian submanifolds.
	www.math.uio.no /nordfjordeid/symplectic.html (517 words)

	Syllabus (Site not responding. Last check: 2007-10-19)
		Lectures on Symplectic Geometry, Ana Cannas da Silva.
		Introduction to Symplectic and Hamiltonian Geometry, Ana Cannas da Silva.
		Symplectic geometry is one of the fastest developing fields in the past two decades.
	www.math.uic.edu /~ruan/math550.htm (108 words)

	The Finsler Geometry Newsletter - Home Page (Site not responding. Last check: 2007-10-19)
		The aim of the Newsletter is to promote the interaction between researchers in convex, integral, metric, and symplectic geometry by providing them with a quick, accessible medium for communicating ideas, announcements, examples, counter-examples, and remarks.
		The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations by Yan Yan Li and Louis Nirenberg.
		I say prematurely because in 1854 Minkowski's work on normed spaces and convex bodies was still forty three years away, and thus not even the infinitesimal geometry on which Finsler manifolds are based was understood at the time.
	www.math.poly.edu /research/finsler (264 words)

	School of Mathematics - Symplectic Geometry and Holomorphic Curves
		The goal of the program is to explore different aspects of the theory of holomorphic curves and their interaction.
		A special accent will be made on applications to Symplectic geometry in low-dimensional topology.
		The time and length of both the seminars and the courses may very depending on the request of speakers, other competing seminars etc. Please consult the weekly IAS seminar e-mail or the IAS seminar page for exact times.
	math.ias.edu /pages/activities/special-programs/symplectic-geometry-and-holomorphic-curves.php (287 words)

	Symplectic Geometry and GR (Site not responding. Last check: 2007-10-19)
		Symplectic Geometry and GR Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
		Symplectic Geometry and GR Subject: Symplectic Geometry and GR From: Eric Forgy
		Hello, If I understand correctly, general relativity in its original form was set within the framework of pseudo-Riemannian geometry ("distances" on a 4-d Lorentzian manifold are not necessarily positive).
	www.lns.cornell.edu /spr/1999-02/msg0015051.html (163 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-19)
		adapted to the symplectic structure (that is, frames with respect to which
		is sometimes included in the definition of a symplectic structure.
		Mostly, for a symplectic structure on a manifold the defining
	eom.springer.de /s/s091860.htm (314 words)

	Courant Symplectic Geometry Seminar (Site not responding. Last check: 2007-10-19)
		Symplectic Vortices on the Complex Plane and Quantum Cohomology: Part I
		The symplectic 2-torus as a Poisson Lie "group"
		The almost C^\infinity regularity of homogeneous MA equation (arising from Kähler geometry) and its application (abstract)
	www.cims.nyu.edu /~albers/courant_symplectic_seminar.html (210 words)

	[No title]
		Geometry of Lagrangian Submanifolds, April 14 - 18, 2003
		Geometry and Physics of G2 Manifolds, April 29 - May 2, 2003
		Symplectic geometry originated as a mathematical outgrowth of Hamiltonian mechanics and dynamical systems and their applications to the theory of elementary particles, oceanographic and atmospheric sciences, condensed matter, accelerator and plasma physics and other disciplines at the classical and quantum levels.
	www.ipam.ucla.edu /programs/sgp2003 (447 words)

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