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196
Localization of gauge theory on a foursphere and supersymmetric Wilson loops
, 2007
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Equivariant Cohomology, Koszul Duality, and the Localization Theorem
 Invent. Math
, 1998
"... This paper concerns three aspects of the action of a compact group K on a space ..."
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Cited by 268 (4 self)
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This paper concerns three aspects of the action of a compact group K on a space
Symplectic surgery and GromovWitten invariants of CalabiYau 3folds
 I, Invent. Math
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Lectures on 2D YangMills Theory, Equivariant Cohomology and Topological Field Theories
, 1996
"... These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying ..."
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Cited by 141 (11 self)
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These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
SasakiEinstein manifolds and volume minimisation
, 2006
"... We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian ..."
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Cited by 118 (7 self)
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We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi–Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat– Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki–Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n = 3 these results provide, via AdS/CFT, the geometric counterpart of a–maximisation in four dimensional superconformal field theories. We also show that our variational problem dynamically sets to zero the Futaki
Hamiltonian 2forms in Kähler geometry, III Compact Examples
, 2008
"... We study the explicit construction of certain types of extremal Kähler metrics on compact complex manifolds. The Kähler metrics we construct have in common the presence of a nontrivial hamiltonian 2form: such 2forms were introduced and studied in previous papers in the series, but this paper is ..."
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Cited by 71 (8 self)
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We study the explicit construction of certain types of extremal Kähler metrics on compact complex manifolds. The Kähler metrics we construct have in common the presence of a nontrivial hamiltonian 2form: such 2forms were introduced and studied in previous papers in the series, but this paper is to a large extent independent. The complex manifolds are all total spaces of projective bundles, and the metrics are adapted to this bundle structure. We focus in particular on constant scalar curvature (CSC) metrics and weakly Bochnerflat (WBF) metrics. We obtain new examples of CSC metrics and nonexistence results which provide a test of the rapidly developing theory of stability for projective varieties. For WBF metrics (i.e., Kähler metrics with coclosed Bochner tensor), a ‘normalized ’ Ricci form is automatically a hamiltonian 2form which is nontrivial unless the metric is Kähler–Einstein and so our constructions have the potential to yield classification results. We obtain such a classification result for compact WBF Kähler 6manifolds, extending earlier work by the first three authors on weakly selfdual Kähler 4manifolds.
The Spectrum of Coupled Random Matrices
, 1999
"... this paper, we will use the following operators e ..."
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Cited by 58 (12 self)
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this paper, we will use the following operators e
Periodic Hamiltonian flows on four dimensional manifolds
, 1998
"... We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S 1spaces. Additionally, we show that all these spaces are Kähler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if th ..."
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Cited by 55 (8 self)
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We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S 1spaces. Additionally, we show that all these spaces are Kähler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.
Littelmann paths and Brownian paths
, 2004
"... We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber. ..."
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Cited by 54 (2 self)
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We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.