Compositio mathematica, ISSN 0010-437X, 9/2006, Volume 142, Issue 5, pp. 1263 - 1285

We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern...

Donaldson maps | Gromov-Witten | Sheaves | MATHEMATICS | sheaves | INVARIANTS

Donaldson maps | Gromov-Witten | Sheaves | MATHEMATICS | sheaves | INVARIANTS

Journal Article

Geometry and Topology, ISSN 1465-3060, 03/2018, Volume 22, Issue 3, pp. 1759 - 1836

.... This action encodes the Gromov-Witten theory of X in purely geometrical terms and induces an action on the derived category Qcoh(X...

Higher category | Gromov-Witten theory | Derived algebraic geometry | Mathematics

Higher category | Gromov-Witten theory | Derived algebraic geometry | Mathematics

Journal Article

2005, International series of monographs on physics, ISBN 9780198568490, Volume 131, xii, 197

This book provides an introduction to some of the most recent developments in string theory, and in particular to their mathematical implications...

String models | Gauge fields (Physics) | Three-manifolds (Topology) | Calabi-yau | Three-manifold geometry | String theories | Gauge theories | Gromov-witten | Knot theory | Chern-simons theory | Enumerative geometry

String models | Gauge fields (Physics) | Three-manifolds (Topology) | Calabi-yau | Three-manifold geometry | String theories | Gauge theories | Gromov-witten | Knot theory | Chern-simons theory | Enumerative geometry

Book

Advances in Mathematics, ISSN 0001-8708, 02/2020, Volume 361, p. 106914

For a Fermat quasi-homogeneous polynomial, we study the associated weighted Fan–Jarvis–Ruan–Witten theory with narrow insertions...

Hassett's moduli | Wall-crossing | Landau-Ginzburg theory | MATHEMATICS | CYCLES | GROMOV-WITTEN INVARIANTS | MODULI SPACES

Hassett's moduli | Wall-crossing | Landau-Ginzburg theory | MATHEMATICS | CYCLES | GROMOV-WITTEN INVARIANTS | MODULI SPACES

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 7/2019, Volume 2019, Issue 7, pp. 1 - 42

We compute the elliptic genus of the D1/D7 brane system in flat space, finding a non-trivial dependence on the number of D7 branes, and provide an F-theory interpretation of the result...

Brane Dynamics in Gauge Theories | Supersymmetric Gauge Theory | Field Theories in Lower Dimensions | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GROMOV-WITTEN THEORY | N=2 GAUGE-THEORIES | PARTITION-FUNCTIONS | GENERA | PHYSICS, PARTICLES & FIELDS | Toruses | M theory | Quantum mechanics | Dependence | Mechanical systems | Invariants | Branes

Brane Dynamics in Gauge Theories | Supersymmetric Gauge Theory | Field Theories in Lower Dimensions | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GROMOV-WITTEN THEORY | N=2 GAUGE-THEORIES | PARTITION-FUNCTIONS | GENERA | PHYSICS, PARTICLES & FIELDS | Toruses | M theory | Quantum mechanics | Dependence | Mechanical systems | Invariants | Branes

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 05/2012, Volume 217, Issue 1020, pp. 1 - 212

Donaldson-Thomas invariants DT alpha(tau) are integers which 'count' tau-stable coherent sheaves with Chern character a on a Calabi-Yau 3-fold X, where tau...

Semistable | Calabi-Yau 3-fold | Vector bundle | Artin stack | Moduli space | Gieseker stability | Donaldson-Thomas invariant | Stability condition | Coherent sheaf | moduli space | BUNDLES | REPRESENTATIONS | DEFORMATION | MODULI SPACES | stability condition | semistable | MATHEMATICS | vector bundle | GROMOV-WITTEN THEORY | COHOMOLOGY | coherent sheaf | CHERN CLASSES | STABILITY CONDITIONS | ABELIAN CATEGORIES | CONFIGURATIONS

Semistable | Calabi-Yau 3-fold | Vector bundle | Artin stack | Moduli space | Gieseker stability | Donaldson-Thomas invariant | Stability condition | Coherent sheaf | moduli space | BUNDLES | REPRESENTATIONS | DEFORMATION | MODULI SPACES | stability condition | semistable | MATHEMATICS | vector bundle | GROMOV-WITTEN THEORY | COHOMOLOGY | coherent sheaf | CHERN CLASSES | STABILITY CONDITIONS | ABELIAN CATEGORIES | CONFIGURATIONS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2016, Volume 288, pp. 201 - 239

We introduce a modular completion of the stack of maps from stable marked curves to the quotient stack [pt/C×], and use this stack to construct some...

Gauge theory | Gromov–Witten | K-theory | Artin stack | Sheaf cohomology | Gromov-Witten | INVARIANTS | DEGENERATIONS | STACKS | MATHEMATICS | STABLE CURVES | MAPS | MODELS | MODULI SPACE | VECTOR-BUNDLES

Gauge theory | Gromov–Witten | K-theory | Artin stack | Sheaf cohomology | Gromov-Witten | INVARIANTS | DEGENERATIONS | STACKS | MATHEMATICS | STABLE CURVES | MAPS | MODELS | MODULI SPACE | VECTOR-BUNDLES

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 2009, Volume 809, Issue 3, pp. 452 - 518

We study the relation between Donaldson–Thomas theory of Calabi–Yau threefolds and a six-dimensional topological Yang–Mills theory...

GROMOV-WITTEN THEORY | CALABI-YAU | QUANTUM | SHEAVES | PHYSICS, PARTICLES & FIELDS

GROMOV-WITTEN THEORY | CALABI-YAU | QUANTUM | SHEAVES | PHYSICS, PARTICLES & FIELDS

Journal Article

American Journal of Mathematics, ISSN 0002-9327, 10/2008, Volume 130, Issue 5, pp. 1337 - 1398

.... They adapted the theory to algebraic geometry, using Chow rings and the language of stacks. It is then their main purpose to complete the work and lay the algebro-geometric...

Morphisms | Homomorphisms | Algebra | Spatial points | Quotients | Functors | Mathematical rings | Inertia | Automorphisms | Gromov-Witten invariants | Algebraic stacks | SPACE | MATHEMATICS | COHOMOLOGY | INVARIANTS | ALGEBRAIC STACKS | STABLE MAPS | VARIETIES | COVERS | INTERSECTION THEORY | CURVES | ARTIN STACKS | Space and time | Research | Invariants | Equations | Geometry | Theorems

Morphisms | Homomorphisms | Algebra | Spatial points | Quotients | Functors | Mathematical rings | Inertia | Automorphisms | Gromov-Witten invariants | Algebraic stacks | SPACE | MATHEMATICS | COHOMOLOGY | INVARIANTS | ALGEBRAIC STACKS | STABLE MAPS | VARIETIES | COVERS | INTERSECTION THEORY | CURVES | ARTIN STACKS | Space and time | Research | Invariants | Equations | Geometry | Theorems

Journal Article

Compositio mathematica, ISSN 0010-437X, 03/2018, Volume 154, Issue 3, pp. 595 - 620

... maps is virtually birational, and, as a consequence, the Gromov–Witten theories with primary insertions coming from $X$ coincide (see Corollary 1.3.1). If $X...

Gromov-Witten theory | birational transformations | stable maps | logarithmic structures | MATHEMATICS | MAPS | BLOW-UPS | CURVES | PAIRS | SCHEMES

Gromov-Witten theory | birational transformations | stable maps | logarithmic structures | MATHEMATICS | MAPS | BLOW-UPS | CURVES | PAIRS | SCHEMES

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 06/2018, Volume 108, Issue 6, pp. 1383 - 1405

... (Kimura and Pestun in Quiver W-algebras, 2015. arXiv: 1512.08533 [hep-th]) with six-dimensional gauge theory.

W-algebras | Supersymmetric gauge theories | Quiver | Conformal field theories | Instanton | Quantum groups | QUANTUM | DONALDSON-THOMAS THEORY | PHYSICS, MATHEMATICAL | VIRASORO | GROMOV-WITTEN THEORY | SYMMETRY | DEFORMATIONS | Algebra

W-algebras | Supersymmetric gauge theories | Quiver | Conformal field theories | Instanton | Quantum groups | QUANTUM | DONALDSON-THOMAS THEORY | PHYSICS, MATHEMATICAL | VIRASORO | GROMOV-WITTEN THEORY | SYMMETRY | DEFORMATIONS | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2019, Volume 355, p. 106765

The Gromov-Witten theory of threefolds admitting a smooth K3 fibration can be solved in terms of the Noether-Lefschetz intersection numbers of the fibration and the reduced invariants of a K3 surface...

Gromov-Witten theory | Quasi-modular forms | Elliptic fibrations | K3 surfaces | MATHEMATICS | VARIETIES | GEOMETRY

Gromov-Witten theory | Quasi-modular forms | Elliptic fibrations | K3 surfaces | MATHEMATICS | VARIETIES | GEOMETRY

Journal Article

13.
Full Text
Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings

Fortschritte der Physik, ISSN 0015-8208, 06/2014, Volume 62, Issue 5‐6, pp. 455 - 540

In these lectures I present a review of non‐perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models...

PERTURBATION-THEORY | GROMOV-WITTEN THEORY | PHYSICS, MULTIDISCIPLINARY | INSTANTONS | BEHAVIOR | PHASE-TRANSITION | EXPANSION | CPN-1 MODELS | STOKES PHENOMENON | LARGE-ORDER | GRAVITY

PERTURBATION-THEORY | GROMOV-WITTEN THEORY | PHYSICS, MULTIDISCIPLINARY | INSTANTONS | BEHAVIOR | PHASE-TRANSITION | EXPANSION | CPN-1 MODELS | STOKES PHENOMENON | LARGE-ORDER | GRAVITY

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2017, Volume 369, Issue 9, pp. 6631 - 6659

... stable sheaves on Calabi-Yau 3-folds, which are related to many other interesting subjects, including the Gopakumar-Vafa conjecture on BPS numbers in string theory...

MATHEMATICS | GROMOV-WITTEN THEORY | BUNDLES | INVARIANTS | MODULI | SHEAVES | DEGENERATION | SCHEMES

MATHEMATICS | GROMOV-WITTEN THEORY | BUNDLES | INVARIANTS | MODULI | SHEAVES | DEGENERATION | SCHEMES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2017, Volume 314, pp. 48 - 70

We study orientability issues of moduli spaces from gauge theories on Calabi–Yau manifolds. Our results generalize and strengthen those for Donaldson...

Moduli spaces of sheaves | Gauge theory | Calabi–Yau manifolds | Dirac operators | Orientability | Shifted symplectic structures | MATHEMATICS | GROMOV-WITTEN THEORY | Calabi-Yau manifolds | DONALDSON-THOMAS THEORY | MODULI SPACES | SHEAVES

Moduli spaces of sheaves | Gauge theory | Calabi–Yau manifolds | Dirac operators | Orientability | Shifted symplectic structures | MATHEMATICS | GROMOV-WITTEN THEORY | Calabi-Yau manifolds | DONALDSON-THOMAS THEORY | MODULI SPACES | SHEAVES

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 9/2015, Volume 2015, Issue 9, pp. 1 - 65

...., D-branes, preserving B-type supersymmetries. We explain how to compute the hemisphere partition function for each object in the derived category of equivariant coherent sheaves, and argue that it depends only on its K theory class...

D-branes | String Duality | Supersymmetric gauge theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | YANG-MILLS THEORY | GAUGE-THEORIES | ALGEBRAS | MODELS | GROMOV-WITTEN INVARIANTS | PARTITION-FUNCTIONS | VACUA | PHYSICS, PARTICLES & FIELDS

D-branes | String Duality | Supersymmetric gauge theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | YANG-MILLS THEORY | GAUGE-THEORIES | ALGEBRAS | MODELS | GROMOV-WITTEN INVARIANTS | PARTITION-FUNCTIONS | VACUA | PHYSICS, PARTICLES & FIELDS

Journal Article

Michigan Mathematical Journal, ISSN 0026-2285, 11/2017, Volume 66, Issue 4, pp. 831 - 854

We study higher-genus Fan-Jarvis-Ruan-Witten theory of any chain polynomial with any group of symmetries...

MATHEMATICS | LOCALIZATION | GROMOV-WITTEN INVARIANTS | CURVES

MATHEMATICS | LOCALIZATION | GROMOV-WITTEN INVARIANTS | CURVES

Journal Article

Japanese Journal of Mathematics, ISSN 0289-2316, 3/2019, Volume 14, Issue 1, pp. 67 - 133

...Japan. J. Math. 14, 67–133 (2019) DOI: 10.1007/s11537-018-1744-8 T akagi Lectures on Donaldson–Thomas theory ? Andrei Okounkov Received: 16 February 2018...

Mathematics, general | Mathematics | History of Mathematical Sciences | Donaldson–Thomas theory | 14N35 | CASSON INVARIANT | MATHEMATICS | GAUGE-THEORIES | Donaldson-Thomas theory | GROMOV-WITTEN THEORY | HILBERT SCHEME | QUANTUM COHOMOLOGY | INSTANTONS | QUIVER VARIETIES | CALABI-YAU | MIRROR SYMMETRY | GEOMETRY

Mathematics, general | Mathematics | History of Mathematical Sciences | Donaldson–Thomas theory | 14N35 | CASSON INVARIANT | MATHEMATICS | GAUGE-THEORIES | Donaldson-Thomas theory | GROMOV-WITTEN THEORY | HILBERT SCHEME | QUANTUM COHOMOLOGY | INSTANTONS | QUIVER VARIETIES | CALABI-YAU | MIRROR SYMMETRY | GEOMETRY

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 5/2016, Volume 2016, Issue 5, pp. 1 - 29

I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of...

Black Holes in String Theory | D-branes | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GROMOV-WITTEN THEORY | DONALDSON-THOMAS THEORY | POINTS | PHYSICS, PARTICLES & FIELDS | String theory | Supersymmetry | Enumeration | Texts | Black holes (astronomy) | Entropy | Localization | Supergravity | Invariants | Physics - High Energy Physics - Theory | hep-th | Nuclear and High Energy Physics | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Black Holes in String Theory | D-branes | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GROMOV-WITTEN THEORY | DONALDSON-THOMAS THEORY | POINTS | PHYSICS, PARTICLES & FIELDS | String theory | Supersymmetry | Enumeration | Texts | Black holes (astronomy) | Entropy | Localization | Supergravity | Invariants | Physics - High Energy Physics - Theory | hep-th | Nuclear and High Energy Physics | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 10/2019, Volume 2019, Issue 10, pp. 1 - 28

... , which is the large N duality of Chern-Simons theory for a framed unknot with integer framing τ in S 3...

Topological Strings | String Duality | Quantum Physics | Quantum Field Theories, String Theory | Chern-Simons Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MARINO-VAFA | COHOMOLOGICAL HALL ALGEBRA | PROOF | ENUMERATION | KNOT | CURVES | CONJECTURE | GROMOV-WITTEN INVARIANTS | INTEGRALITY | PHYSICS, PARTICLES & FIELDS | Integers | Field theory (physics) | Framing | Strings | Invariants | Quantum theory

Topological Strings | String Duality | Quantum Physics | Quantum Field Theories, String Theory | Chern-Simons Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MARINO-VAFA | COHOMOLOGICAL HALL ALGEBRA | PROOF | ENUMERATION | KNOT | CURVES | CONJECTURE | GROMOV-WITTEN INVARIANTS | INTEGRALITY | PHYSICS, PARTICLES & FIELDS | Integers | Field theory (physics) | Framing | Strings | Invariants | Quantum theory

Journal Article