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Topic: Hodge theory

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	Hodge Theory and the Art of Paper Folding - Kapovich, Millson (ResearchIndex)
		Abstract: Using Hodge theory and L 2 -cohomology we study the singularities and topology of configuration and moduli spaces of polygonal linkages in the 2-sphere.
		12 The deformation theory of representations of fundamental gro..
		4 the deformation theory of representations of fundamental gro..
	citeseer.ist.psu.edu /kapovich96hodge.html (620 words)

	No Title
		Intermediate Jacobians and the Hodge conjecture for cubic fourfolds.
		In: Hodge Theory: Proceedings, Sant Cugat, Spain, 1985.
		The Hodge structures on the intersection homology of varieties with isolated singularities.
	www.math.jhu.edu /~sz/PP/vita.html (541 words)

	PlanetMath: Hodge theory
		Hodge theory is a branch of algebraic geometry and complex manifold theory that deals with the decomposition of the cohomology groups of an complex projective
		A example of a class of manifolds where this holds true is Kahler Manifolds, which are complex manifolds with a Riemannian metric that is compatible with the complex structure.
		This is version 9 of Hodge theory, born on 2005-06-22, modified 2007-09-30.
	planetmath.org /encyclopedia/HodgeTheory.html (431 words)

	What is Knowledge? A Debate - Paul Rezedes and Mitch Hodge with Graham Dennis - The Examined Life On-Line Philosophy ...
		Hodge has not adequately silenced the many objections to it (for instance, the Gettier cases), and thus, although the JTB model may have some validity as a rule of thumb, the model itself does not serve as the ultimate arbiter or standard for deciding what knowledge is.
		Hodge’s notions is a commitment to the notion of direct cognitive presence. This commitment appears in his offering at the Journal, for our consideration, the Butchvarov argument for primary epistemic judgments. It also appears when he asserts the absurdity of the notion that one might not believe what one believes. Mr.
		Hodge notes in footnote 1 that the JTB model works with theories of truth other than correspondence theory. To be sure, the Gettier cases can be treated as neutral with respect to the theory of truth at issue, and thus Mr.
	examinedlifejournal.com /archives/vol2ed6/debate3.html (2105 words)

	Reformation21 »
		No doubt it is tautologically true that Hodge was a child of his time, and no doubt he could have benefited from the philosophy of science of children of later times, which claims that scientific theories are falsifiable hypotheses, not inductive generalizations from the data.
		Hodge is concerned to distinguish what he believes to be the correct systematic theological method from two other methods which he calls, somewhat imprecisely as he acknowledges, the 'Speculative' and the 'Mystical'.
		However, Hodge refers to 'the truths' of the Bible, and 'the facts of Scripture', and I suppose that he would not deny that these truths and facts are expressed, or are expressible, in propositions.
	reformation21.com /Counterpoints/Counterpoints/234/vobId__3719 (3567 words)

	Charles Hodge and His Objection to Darwinism: The Exclusion of Intelligent Design
		Charles Hodge was born to Hugh and Mary Hodge in Philadelphia in December 1797.
		Hodge defines design to be "the intelligent and voluntary selection of an end, and the intelligent and voluntary choice, application, and control of means appropriate to the accomplishment of that end." That design implies intelligence is part of its very nature.
		He confirms both that Hodge was correct in his understanding of Darwinism (as defined by Darwin himself) and Christianity (as the mainstream theology throughout its history has understood it) as fundamentally incompatible and that Hodge did accurately represent Christian theological tradition as a whole (Wells 1988:215-223).
	www.theropps.com /papers/Winter1997/CharlesHodge.htm (2836 words)

	introhodge
		Since its introduction, Hodge theory and its variants (variations of Hodge structures, mixed Hodge structures, variations of mixed Hodge structures) have been a source of some of the deepest results in algebraic geoemetry.
		More recently the theory of variations of Hodge structures has served as the basis of the theory of Shimura varieties, and, similarly, mixed Hodge structures form a basis for a theory of mixed Shimura varieties, important for the theory of compactifications.
		The book under review is a collection of three articles about Hodge theory and related developments, which are all aimed at non-experts and fulfill, in an extremely satisfactory manner, two functions.
	www-fourier.ujf-grenoble.fr /~peters/mirror.f/introhodge/introhodge.html (786 words)

	Hodge, Roger D. (Harper's Magazine)
		Hodge also brought a new emphasis on contemporary art to the magazine, and came to treat the artwork published in each issue of the Readings section as a carefully curated exhibit of paintings and photographs drawn from galleries all around the world.
		Hodge was born in 1967 and raised in Del Rio, Texas, where his family has been in the ranching business for five generations.
		Hodge received a master’s degree for a thesis on the logic of Aristotle’s metaphysics but abandoned his dissertation on Spinoza’s theory of freedom to work at Harper’s Magazine.
	www.harpers.org /subjects/RogerDHodge (356 words)

	Politically Dead Wrong. Origins & Design 17:2. Wells, Jonathan
		But Hodge's opposition to Darwinism was actually based on a notion of design which is central to the Christian tradition, and pervades the writings of every major theologian, so it is a mistake to dismiss him as provincial and outmoded.
		This is the essence of Hodge's critique of Darwinism.
		Hodge wrote in the heat of intellectual battle, however, when the issues were at least as confusing as they are now.
	www.arn.org /docs/odesign/od172/wells172.htm (1390 words)

	Graduate: Math Department, WCAS, Northwestern University
		This course is an introduction to abstract ergodic theory, focusing on the asymptotic behavior of measure preserving transformations.
		This course will be an introduction, through examples, to some of the ideas of the modern theory of stacks, and to some of the abstract ideas (simplicial sheaves, closed model categories, cosimplicial spaces, homotopy diagrams and their rectification) which are at the heart of a large part of contemporary research in geometry and topology.
		In some sense this second phase was the golden era of Hodge theory and since the mid 1970's the subject has played a less central role in mathematics.
	math.northwestern.edu /graduate/Syllabi/winter07.html (1132 words)

	Matches for: (Site not responding. Last check: 2007-10-30)
		Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds.
		The material leads the reader to the forefront of research in many areas related to Hodge theory, and that in a detailed highly self-contained manner...
		First, the basic methods used in the theories are discussed and developed in great detail; second, some newer developments are described, giving the reader a good overview of the more important applications.
	www.mathaware.org /bookstore?fn=20&arg1=smfamsseries&item=SMFAMS-8 (504 words)

	Untitled Document
		The International Centre for Mathematical Sciences, Edinburgh, held a conference from 20-26 July, to commemorate the centenary of Sir William Hodge, the originator of Hodge theory – ‘one of the landmarks in the history of mathematics in the 20th century’ according to Hermann Weyl.
		There was a quite spectacular array of speakers, including four Fields Medallists, the world’s leading experts in Hodge theory, former colleagues and students of Hodge such as Fritz Hirzebruch and Sir Roger Penrose, and members of the Hodge family.
		Hodge was born in Edinburgh and spent most of his academic career in Cambridge.
	www.lms.ac.uk /newsletter/319/319_02.html (989 words)

	Guitar Columns by David Hodge Lessons - Guitar Noise
		David Hodge's core philosophy is that music is meant to be shared and his columns are in written in a wonderfully down-to-earth style that is fun to read and loaded with practical examples.
		By David Hodge It is much more important to know how and why something works than it is to "just do it." But the sad fact is that most guitarists truly believe that the art of playing well is strictly a matter for the hands.
		By David Hodge The trick to being a better guitarist is you have to be able to work both inside and outside of the box.
	www.guitarnoise.com /columns.php (4136 words)

	Theology of the Shorter Catechism. A. A. Hodge and J. A. Hodge -- Theory of Refracting Telescopes: in Cornell ...
		The Theory of Human Progression, and Natural Probability of a Reign of Justice.
		Theory of Morals: An inquiry concerning the law of moral distinction and the variations and the contradictions of ethical codes.
		Theory of Pneumatology: IN reply to the Question "What ought to be Believed or Disbelieved.
	moa.cit.cornell.edu /moa/browse.author/t.64.html (129 words)

	Hodge theory and complex algebraic geometry II \| LibraryThing
		Hodge theory and complex algebraic geometry II
		This is a modern introduction to Kaehlerian geometry and Hodge structure.
		Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry).
	www.librarything.com /isbn/0521802601 (183 words)

	Questions I'm thinking about
		Rigid cohomology is a cohomology theory for algebraic varieties over fields of positive characteristic that plays a role similar to that of algebraic de Rham cohomology for varieties over fields of characteristic zero.
		It was constructed by Berthelot based primarily on Dwork's proof of the rationality of the zeta function of an algebraic variety (though it also draws from the theory of crystalline cohomology, constructed largely by Berthelot at the behest of Grothendieck).
		Hodge theory is the study of the special structure of those vector spaces, and families of vector spaces, which occur as the cohomology of algebraic varieties over the complex numbers.
	www-math.mit.edu /~kedlaya/questions.html (1589 words)

	Hodge Theory and Complex Algebraic Geometry II - Cambridge University Press
		Hodge Theory and Complex Algebraic Geometry II Series: Cambridge Studies in Advanced Mathematics (No. 77)
		The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties.
		The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles.
	www.cup.cam.ac.uk /catalogue/catalogue.asp?isbn=0521802830 (511 words)

	Hodge theory in the Sobolev topology for the De Rham complex on a smoothly bounded domain in Euclidean Space (Site not responding. Last check: 2007-10-30)
		Hodge theory in the Sobolev topology for the De Rham complex on a smoothly bounded domain in Euclidean space
		The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied.
		Next, the Hodge theory of the $\overline{\partial}$- Neumann problem in the Sobolev topology is studied.
	www.emis.de /journals/ERA-AMS/1995-03-002/1995-03-002.html (156 words)

	Hodge Theory Working Seminar
		William Hodge showed that the homology of a compact smooth algebraic manifold has a very rich structure which impacts its topology.
		The goal of this working seminar is to understand Deligne’s influential paper “Theorie de Hodge,II”, starting from scratch.
		March 18, Mario Maican: The Hodge and Lefschetz decompositions of compact Kahler manifolds
	www.nd.edu /~lnicolae/Hodge.htm (152 words)

	Mathematical Sciences Research Institute - Non-Abelian Hodge Theory (Site not responding. Last check: 2007-10-30)
		Together with his students and collaborators, Simpson developed the theory of geometric n-stacks in a form which is particularly well adapted to understanding non-abelian cohomology of complex algebraic varieties as well as their Hodge structures.
		An indication of the power of the theory is that even though the notion of a geometric n-stack was invented for the task of understanding non-abelian Hodge structures it immediately acquired a life of its own and keeps popping up in different areas of modern mathematics.
		All these indicate that until non-abelian Hodge theory has reached is full maturity it will provide us with new restrictions on the homotopy types and the monodromy of the projective varieties.
	zeta.msri.org /calendar/workshops/WorkshopInfo/140/show_workshop (445 words)

	THE HODGE THEORY OF PROJECTIVE MANIFOLDS
		This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.
		Though the proof of the Hodge Theorem is omitted, its consequences — topological, geometrical and algebraic — are discussed at some length.
		Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
	www.worldscibooks.com /mathematics/p508.html (219 words)

	Hodge theory Books
		Hodge Theory in the Sobolev Topology for the De Rham Complex
		Algebraic Cycles and Hodge Theory : Lectures Given at the 2nd Session of the Centro Internazionale Matematico Estivo
		Algebraic Cycles and Hodge Theory : Lectures Given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Torino, Italy, June 21-29, 1993
	www.allbookstores.com /Hodge_Theory.html (232 words)

	Introduction
		The main subjects covered are Hodge theory, heat operators for Laplacians on forms, and the Chern-Gauss-Bonnet theorem in detail.
		In particular, by the Hodge theorem the dimension of the kernel of
		This proof assumes the existence of an integral kernel, the heat kernel, for heat flow for the Laplacians on forms; the construction of the heat kernel is in Chapter 3.
	math.bu.edu /people/sr/webbook/node2.html (1894 words)

	Hodge theory and algebraic cycles (Site not responding. Last check: 2007-10-30)
		The Hodge structure of a complex manifold contains detailed information, and Griffiths' Torelli principle says that in many cases it should be enough to determine the manifold.
		The primary motivation for the study of algebraic cycles is the famous unsolved Hodge conjecture; work on this has led to new subjects such as motives, relations to K theory and D-modules.
		Progress is expected from the overlap between algebraic cycles and problem areas (e, g, h, j, m), for example, related to motivic integration, elliptic genus and Fourier-Mukai transforms.
	euclid.mathematik.uni-kl.de /NEW/node26.html (207 words)

	K-theory Calendar
		Evanston, September 16 - 19, 2004, Algebraic Cycles, K-Theory, and Modular Representation Theory in Honor of the 60th birthday of Eric Friedlander.
		Palo Alto, April 23 - 26, 2004, Theory of motives, homotopy theory of varieties, and dessins d'enfants.
		Berkeley, Homotopy theory for algebraic varieties with applications to K-theory and quadratic forms, Mathematical Sciences Research Institute, May 12-16, 1998.
	www.math.uiuc.edu /K-theory/Calendar (1377 words)

	Matches for: (Site not responding. Last check: 2007-10-30)
		The conference presented some of the best recent research in algebraic $K$-theory, Hodge theory, motivic cohomology and polylogarithms.
		Articles explore the frontiers of motivic cohomology and motivic homotopy theory, the periods of modular forms and the variational aspects of Hodge theory.
		Contributions include a program paper of V. Voevodsky outlining the outstanding open questions in the stable homotopy theory of motives, as well as papers on motivic cohomology, Galois cohomology and algebraic differential characters by A. Beilinson, S. Bloch, F. Bogomolov, H.
	www.mathaware.org /bookstore?fn=20&arg1=inprseries&item=INPR-52-1 (260 words)

	Research (Site not responding. Last check: 2007-10-30)
		In our non-compact hyperkähler case even an integration theory was missing; which has recently been adressed in a joint paper with Proudfoot.
		Is there a Hodge theoretical L^2-index interpretation of a certain signature, which can be defined on circle compact manifolds using the integration technique in my recent paper with Proudfoot?
		I conjecture that for a hyper-compact hyperkähler manifold this signature is always non-positive if the quaternionic dimension is odd and is non-negative if the quaternionic dimension is even; a result which is known for the L^2-signature by a result of Hitchin.
	www.ma.utexas.edu /users/hausel/research.html (486 words)

	Gregory Pearlstein, Visiting Assistant Professor
		I study the geometry and arithemtic of algebraic varieties using Hodge theory (i.e.
		SL_2 orbits and degenerations of mixed Hodge structure, Journal of Differential Geometry (Accepted, August, 2005).
		Pearlstein, On the asymptotic behavior of admissible variations of mixed Hodge structure, in Algebraic Geometry in East Asia (2002).
	fds.duke.edu /db/aas/math/gpearlst (126 words)

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