1.
Hodge theory

2014, Mathematical notes, ISBN 9780691161341, Volume 49., xvii, 589

This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics...

Hodge theory | Manifolds (Mathematics) | MATHEMATICS | Group Theory | Topology | Research | Mathematics | Congresses

Hodge theory | Manifolds (Mathematics) | MATHEMATICS | Group Theory | Topology | Research | Mathematics | Congresses

Book

The journal of high energy physics, ISSN 1029-8479, 2018, Volume 2018, Issue 8, pp. 1 - 72

It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance...

Superstring Vacua | Differential and Algebraic Geometry | D-branes | Effective Field Theories | Nuclear and High Energy Physics | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MONODROMY | SUPERGRAVITY | DEGENERATIONS | SINGULARITIES | STRING THEORY | BLACK-HOLES | HODGE STRUCTURE | SWAMPLAND | MANIFOLDS | PHYSICS, PARTICLES & FIELDS | Towers | Couplings | Theorems | Gauge theory | Quantum gravity | Quantum phenomena | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Superstring Vacua | Differential and Algebraic Geometry | D-branes | Effective Field Theories | Nuclear and High Energy Physics | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MONODROMY | SUPERGRAVITY | DEGENERATIONS | SINGULARITIES | STRING THEORY | BLACK-HOLES | HODGE STRUCTURE | SWAMPLAND | MANIFOLDS | PHYSICS, PARTICLES & FIELDS | Towers | Couplings | Theorems | Gauge theory | Quantum gravity | Quantum phenomena | Physics - High Energy Physics - Theory | Nuclear and particle physics. Atomic energy. Radioactivity | High Energy Physics - Theory

Journal Article

Annals of mathematics, ISSN 0003-486X, 2018, Volume 188, Issue 2, pp. 381 - 452

We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann...

Bergman fan | Hard Lefschetz theorem | Hodge-Riemann relation | Matroid | MATHEMATICS | hard Lefschetz theorem | matroid

Bergman fan | Hard Lefschetz theorem | Hodge-Riemann relation | Matroid | MATHEMATICS | hard Lefschetz theorem | matroid

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2011, Volume 127, Issue 1, pp. 203 - 244

... is an analogue of the Laplace operator or scalar Laplacian. We shall study the graph Helmholtzian using combinatorial Hodge theory, which provides...

Hodge Laplacian | Combinatorial Hodge theory | Rank aggregation | 68T05 | 58A14 | Combinatorial Laplacian | Theoretical, Mathematical and Computational Physics | Graph Helmholtzian | Mathematics | Borda count | 90C05 | 90C27 | HodgeRank | Statistical ranking | 91B12 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Discrete exterior calculus | 91B14 | Combinatorics | Kemeny optimization | MATHEMATICS, APPLIED | ALGORITHM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Ranking systems | Statistical data | Studies | Regression analysis | Mathematical programming | Operators | Ranking | Analogue | Mathematical analysis | Graphs | Decomposition | Internet | Combinatorial analysis

Hodge Laplacian | Combinatorial Hodge theory | Rank aggregation | 68T05 | 58A14 | Combinatorial Laplacian | Theoretical, Mathematical and Computational Physics | Graph Helmholtzian | Mathematics | Borda count | 90C05 | 90C27 | HodgeRank | Statistical ranking | 91B12 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Discrete exterior calculus | 91B14 | Combinatorics | Kemeny optimization | MATHEMATICS, APPLIED | ALGORITHM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Ranking systems | Statistical data | Studies | Regression analysis | Mathematical programming | Operators | Ranking | Analogue | Mathematical analysis | Graphs | Decomposition | Internet | Combinatorial analysis

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 09/2014, Volume 29, Issue 24, p. 1450135

Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1...

(quasi-)topological field theory | Curci | Ferrari conditions | Self-duality condition | Hodge theory | Abelian p-form (p = 1, 2, 3) gauge theories | (anti-)BRST symmetries | (dual-)gauge symmetry transformations | (anti-)co-BRST symmetries | DUAL-BRST SYMMETRY | Curci-Ferrari conditions | PHYSICS, NUCLEAR | DECOMPOSITION THEOREM | self-duality condition | COHOMOLOGY | Abelian p-form (p=1, 2, 3) gauge theories | QUANTIZATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

(quasi-)topological field theory | Curci | Ferrari conditions | Self-duality condition | Hodge theory | Abelian p-form (p = 1, 2, 3) gauge theories | (anti-)BRST symmetries | (dual-)gauge symmetry transformations | (anti-)co-BRST symmetries | DUAL-BRST SYMMETRY | Curci-Ferrari conditions | PHYSICS, NUCLEAR | DECOMPOSITION THEOREM | self-duality condition | COHOMOLOGY | Abelian p-form (p=1, 2, 3) gauge theories | QUANTIZATION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Geometry and Topology, ISSN 1465-3060, 03/2017, Volume 21, Issue 2, pp. 841 - 902

.... For a compact Kahler manifold, the C*-completion also gives the natural setting for nonabelian Hodge theory...

Twistor structures | Nonabelian Hodge theory | C-algebras | MATHEMATICS | C-STAR-ALGEBRAS | REPRESENTATIONS | FUNDAMENTAL GROUP | MODULI

Twistor structures | Nonabelian Hodge theory | C-algebras | MATHEMATICS | C-STAR-ALGEBRAS | REPRESENTATIONS | FUNDAMENTAL GROUP | MODULI

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 11/2017, Volume 34, Issue 24, p. 247001

We consider a free p-form gauge theory on a d-dimensional sphere of radius R and calculate its free energy...

gauge theory | PHYSICS, MULTIDISCIPLINARY | hodge duality | sphere partition function | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

gauge theory | PHYSICS, MULTIDISCIPLINARY | hodge duality | sphere partition function | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, ISSN 2193-8407, 03/2020, Volume 15, Issue 1, pp. 249 - 299

We prove that the cyclic homology of a saturated A infinity category admits the structure of a 'polarized variation of Hodge structures', building heavily on...

MATHEMATICS | FORMALITY | K-THEORY | PERIODS | Noncommutative Hodge theory | Mirror symmetry | Mathematics - K-Theory and Homology

MATHEMATICS | FORMALITY | K-THEORY | PERIODS | Noncommutative Hodge theory | Mirror symmetry | Mathematics - K-Theory and Homology

Journal Article

2002, SMF/AMS texts and monographs, ISBN 9780821820407, Volume 8, ix, 232

Book

Journal of High Energy Physics, ISSN 1126-6708, 1/2015, Volume 2015, Issue 1, pp. 1 - 83

The four-form field strength in F-theory compactifications on Calabi-Yau four-folds takes its value in the middle cohomology group H 4...

F-Theory | Flux compactifications | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | ENHANCED GAUGE-SYMMETRY | 4-FOLDS | TORIC GEOMETRY | THEORY COMPACTIFICATIONS | DUALITY | HODGE NUMBERS | VACUA | MIRROR SYMMETRY | PHYSICS, PARTICLES & FIELDS | Mathematics - Algebraic Geometry | Nuclear and High Energy Physics | Algebraic Geometry | Mathematics | High Energy Physics - Theory

F-Theory | Flux compactifications | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | ENHANCED GAUGE-SYMMETRY | 4-FOLDS | TORIC GEOMETRY | THEORY COMPACTIFICATIONS | DUALITY | HODGE NUMBERS | VACUA | MIRROR SYMMETRY | PHYSICS, PARTICLES & FIELDS | Mathematics - Algebraic Geometry | Nuclear and High Energy Physics | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 7/2018, Volume 2018, Issue 7, pp. 1 - 32

...-Kähler compactifications of the theory. This description of the moduli has allowed the explicit computation of the moduli stabilization effects of a wide range of non-trivial gauge bundles on Calabi-Yau three-folds...

Superstring Vacua | Supergravity Models | Flux compactifications | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | ORIENTIFOLDS | SUPERSYMMETRY | COHOMOLOGY | HODGE NUMBERS | CALABI-YAU MANIFOLDS | FLUXES | COMPLETE-INTERSECTIONS | PHYSICS, PARTICLES & FIELDS | String theory | Maps | Identification methods | Supergravity | Physics - High Energy Physics - Theory | High Energy Physics | Symplectic Geometry | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Superstring Vacua | Supergravity Models | Flux compactifications | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | ORIENTIFOLDS | SUPERSYMMETRY | COHOMOLOGY | HODGE NUMBERS | CALABI-YAU MANIFOLDS | FLUXES | COMPLETE-INTERSECTIONS | PHYSICS, PARTICLES & FIELDS | String theory | Maps | Identification methods | Supergravity | Physics - High Energy Physics - Theory | High Energy Physics | Symplectic Geometry | Theory | Nuclear and particle physics. Atomic energy. Radioactivity | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Journal Article

The journal of high energy physics, ISSN 1029-8479, 2019, Volume 2019, Issue 3, pp. 1 - 86

The Swampland Distance Conjecture proposes that approaching infinite distances in field space an infinite tower of states becomes exponentially light. We study...

Superstring Vacua | Differential and Algebraic Geometry | D-branes | Effective Field Theories | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | HODGE | SINGULARITIES | MANIFOLDS | MIRROR SYMMETRY | DEGENERATION | PHYSICS, PARTICLES & FIELDS | Theorems | Orbits | Singularities | Intersections | Loci | Symmetry

Superstring Vacua | Differential and Algebraic Geometry | D-branes | Effective Field Theories | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | HODGE | SINGULARITIES | MANIFOLDS | MIRROR SYMMETRY | DEGENERATION | PHYSICS, PARTICLES & FIELDS | Theorems | Orbits | Singularities | Intersections | Loci | Symmetry

Journal Article

Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 01/2014, Volume 13, Issue 1, pp. 65 - 118

The aim of this article is to study the Bloch–Kato exponential map and the Perrin-Riou big exponential map purely in terms of $(\varphi , \Gamma )$-modules...

Secondary 11F85; 11S25 | 2010 Mathematics subject classification Primary 11F80 | MATHEMATICS | MONODROMY | FIELDS | P-ADIC REPRESENTATIONS | COHOMOLOGY | DIFFERENTIAL-EQUATIONS | B-pair | p-adic Hodge theory | (phi,Gamma)-module | Geometry | Applied mathematics | Algebra | Construction

Secondary 11F85; 11S25 | 2010 Mathematics subject classification Primary 11F80 | MATHEMATICS | MONODROMY | FIELDS | P-ADIC REPRESENTATIONS | COHOMOLOGY | DIFFERENTIAL-EQUATIONS | B-pair | p-adic Hodge theory | (phi,Gamma)-module | Geometry | Applied mathematics | Algebra | Construction

Journal Article

2006, Monographs and textbooks in pure and applied mathematics, ISBN 0849337399, Volume 273, xix, 311

Book

Nuclear Physics, Section B, ISSN 0550-3213, 2011, Volume 850, Issue 1, pp. 214 - 231

Multiply-connected Calabi–Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the...

String theory | Calabi–Yau manifolds | Mirror symmetry | Calabi-Yau manifolds | THREEFOLDS | ORBIFOLDS | SMALL HODGE NUMBERS | MODULI SPACE | CONDENSATION | COMPACTIFICATION | PHYSICS, PARTICLES & FIELDS

String theory | Calabi–Yau manifolds | Mirror symmetry | Calabi-Yau manifolds | THREEFOLDS | ORBIFOLDS | SMALL HODGE NUMBERS | MODULI SPACE | CONDENSATION | COMPACTIFICATION | PHYSICS, PARTICLES & FIELDS

Journal Article

2002, Cambridge studies in advanced mathematics, ISBN 0521802601, Volume 76., ix, 322

.... The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry...

Hodge theory | Geometry, Algebraic

Hodge theory | Geometry, Algebraic

Book

07/2014, Mathematical notes, ISBN 9780691161341

This book provides a comprehensive and up-to-date introduction to Hodge theory--one of the central and most vibrant areas of contemporary mathematics--from leading specialists on the subject...

Hodge theory | Mathematics

Hodge theory | Mathematics

eBook

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, ISSN 0217-751X, 10/2019, Volume 34, Issue 30

We derive the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the system of a toy model of Hodge theory (i.e. a rigid rotor) by exploiting the (anti-)BRST and (anti...

nilpotency property | INVARIANCE | FIELDS | BRS SYMMETRY | PHYSICS, NUCLEAR | absolute anticommutativity property | N=2 SUSY QM symmetries of a free particle | (anti-)BRST and (anti-) co-BRST symmetries | conserved and nilpotent SUSY charges | SUPERFIELD APPROACH | A 1D toy model of Hodge theory (i.e. a rigid rotor) | (anti-)chiral supervariable approach | conserved (anti-)BRST and (anti-)co-BRST charges | (anti-)BRST and (anti-)co-BRST invariant restrictions | TRANSFORMATIONS | PHYSICS, PARTICLES & FIELDS

nilpotency property | INVARIANCE | FIELDS | BRS SYMMETRY | PHYSICS, NUCLEAR | absolute anticommutativity property | N=2 SUSY QM symmetries of a free particle | (anti-)BRST and (anti-) co-BRST symmetries | conserved and nilpotent SUSY charges | SUPERFIELD APPROACH | A 1D toy model of Hodge theory (i.e. a rigid rotor) | (anti-)chiral supervariable approach | conserved (anti-)BRST and (anti-)co-BRST charges | (anti-)BRST and (anti-)co-BRST invariant restrictions | TRANSFORMATIONS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 1/2008, Volume 21, Issue 1, pp. 101 - 136

Journal Article

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