AI & ChatGPT searches , social queries for QUANTUM COHOMOLOGY
Search references for QUANTUM COHOMOLOGY. Phrases containing QUANTUM COHOMOLOGY
See searches and references containing QUANTUM COHOMOLOGY!
Search references for QUANTUM COHOMOLOGY. Phrases containing QUANTUM COHOMOLOGY
See searches and references containing QUANTUM COHOMOLOGY!QUANTUM COHOMOLOGY
Concept in algebraic geometry
symplectic topology and algebraic geometry, a quantum cohomology ring is an extension of the ordinary cohomology ring of a closed symplectic manifold. It comes
Quantum_cohomology
Algebraic structure used in topology
Intersection cohomology Khovanov homology Lie algebra cohomology Local cohomology Motivic cohomology Non-abelian cohomology Quantum cohomology complex-oriented
Cohomology
cohomology l-adic cohomology Lie algebra cohomology Quantum cohomology Sheaf cohomology Singular homology Spencer cohomology Stable Homotopy and Generalised Homology
List_of_cohomology_theories
Concept in string theory
be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been
Gromov–Witten_invariant
naturally in the subject of symplectic topology, more specifically quantum cohomology. The broadest definition is in the category of Riemannian supermanifolds
Frobenius_manifold
Chinese mathematician
Sciences Research Institute. In 1998 he was an Invited Speaker with talk Quantum Cohomology and its Applications at the International Congress of Mathematicians
Yongbin_Ruan
Chinese mathematician (born 1958)
of certain symplectic manifolds.[RT95] This structure is known as quantum cohomology; a contemporaneous and similarly influential approach is due to Dusa
Tian_Gang
(1998). Liu, Xiaobo; Tian, Gang (1998-10-20), Virasoro Constraints For Quantum Cohomology, arXiv:math/9806028, Bibcode:1998math......6028L Getzler, Ezra (1999)
Virasoro_conjecture
South Korean mathematician
Yang-Mills Theory, Seiberg-Witten Theory, Gromov-Witten Theory, and Quantum cohomology of symplectic manifolds. His teaching career includes Chungbuk National
Yong_Seung_Cho
Symplectic topology tool
the relation between Floer homology and quantum cohomology and formulated as the following: The Floer cohomology groups of the loop space of a semi-positive
Floer_homology
specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product
Cohomology_ring
Tools for studying groups based on techniques from algebraic topology
specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic
Group_cohomology
Cohomology with real coefficients computed using differential forms
In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of
De_Rham_cohomology
Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They were introduced by
Schubert_polynomial
Russian mathematician (born 1969)
infinite symmetric groups, the statistics of plane partitions, and the quantum cohomology of the Hilbert scheme of points in the complex plane. Much of his
Andrei_Okounkov
Theory in physics
invariants. Enumerative geometry Gromov–Witten invariant Hilbert scheme Quantum cohomology Bridgeland, Tom (2006-02-08). "Stability conditions on triangulated
Donaldson–Thomas_theory
Mathematical space
c(E)c(F)=1.} The quantum cohomology ring was calculated by Edward Witten. The generators are identical to those of the classical cohomology ring, but with
Grassmannian
Branch of algebraic geometry concerned with counting solutions
other geometric objects, sometimes via the theory of quantum cohomology. The study of quantum cohomology, Gromov–Witten invariants and mirror symmetry gave
Enumerative_geometry
American mathematician
interested in topics in abstract algebra, including Hochschild cohomology[SW99] and quantum groups.[W96][BW04] She is a professor of mathematics at Texas
Sarah_Witherspoon
states that the orbifold cohomology of a Gorenstein orbifold is isomorphic to a semiclassical limit of the quantum cohomology of a crepant resolution.
Crepant_resolution
German mathematician (1953–2025)
Press, 1998. Dusa McDuff: J {\displaystyle J} -holomorphic curves and quantum cohomology. American Mathematical Soc. 1994. ISBN 978-0-8218-0332-5. Dietmar
Dietmar_Salamon
Theory in theoretical physics
invariants, which measure the cup product in a deformed cohomology ring called the quantum cohomology. The string field theory of the A-model closed strings
Topological_string_theory
crystal in solid-state physics, Langmuir oscillations in plasma, quantum cohomology; notable for being a completely integrable system Trachenko-Zaccone
List of nonlinear ordinary differential equations
List_of_nonlinear_ordinary_differential_equations
Mathematical construct
using a closed one-form instead of a function. The notion is used in quantum cohomology, among the others. The Novikov ring Nov ( Γ ) {\displaystyle \operatorname
Novikov_ring
International prize for mathematicians
ISBN 0817638989 2010 – Yuri I. Manin for his Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces, American Mathematical Society, 1999. ISBN 0821819178
Bolyai_Prize
Russian mathematician (1937–2023)
S2CID 250895773. Frobenius manifolds, quantum cohomology, and moduli spaces. American Mathematical Society. 1999. Quantum groups and non commutative geometry
Yuri_Manin
English mathematician
Lalond, François (1996). "Review: J-holomorphic curves and quantum cohomology by Dusa McDuff and Dietmar Salamon" (PDF). Bull. Amer. Math. Soc.
Dusa_McDuff
Geometric space
the moduli space of curves". aimath.org. American Institute of Mathematics. "Moduli of Stable Maps, Gromov-Witten Invariants, and Quantum Cohomology"
Moduli_of_algebraic_curves
Type of topological order in condensed matter physics
Symmetry-protected topological (SPT) order is a kind of order in zero-temperature quantum-mechanical states of matter that have a symmetry and a finite energy gap
Symmetry-protected topological order
Symmetry-protected_topological_order
, n ( X , β ) {\displaystyle {\overline {M}}_{0,n}(X,\beta )} in quantum cohomology. These moduli spaces are smooth orbifolds whenever the target space
Convexity (algebraic geometry)
Convexity_(algebraic_geometry)
{\displaystyle \wedge } . The noncommutative or quantum de Rham cohomology is defined as the cohomology of this complex. A higher order differential calculus
Quantum_differential_calculus
Japanese mathematician and mathematical physicist
research combines the areas of algebraic topology, differential cohomology, and quantum field theory. She is an associate professor at Kyoto University
Mayuko_Yamashita
Russian-American physicist (born 1963)
generalized-cohomology classifications of symmetry-protected topological phases with symmetry group G. Kitaev has also contributed to the study of quantum chaos
Alexei_Kitaev
Equations describing classical electromagnetism
second real cohomology group is 'trivial' (meaning that its form follows from a definition). By the isomorphism with the second de Rham cohomology this condition
Maxwell's_equations
Generalisation of a sheaf; a fibered category that admits effective descent
Massarenti, Alez. "Moduli of Stable Maps, Gromov-Witten Invariants, and Quantum Cohomology" (PDF). pp. 1–4. Archived (PDF) from the original on 2018-01-23. Fantechi
Stack_(mathematics)
American annual mathematics conference
torsion free connections Matthias Schwarz, Symplectic fixed points and quantum cohomology Stephen Semmes, Geometry with little smoothness Scott Axelrod, Generalized
Geometry_Festival
Concept in algebraic geometry
Gromov-Witten Invariants". In de Bartolomeis; Dubrovin; Reina (eds.). Quantum Cohomology. Lecture Notes in Mathematics. Vol. 1776. Berlin: Springer. pp. 3–38
Moduli stack of vector bundles
Moduli_stack_of_vector_bundles
Algebraic theory
information. Often, this revolves around using categorical structures or cohomology theories to classify and describe various topological phases of matter
Algebraic theory of topological quantum information
Algebraic_theory_of_topological_quantum_information
Concept in mathematics
curves is significant in applications to symplectic geometry and quantum cohomology. The techniques used by Richard Schoen and Uhlenbeck to study the
Harmonic_map
Group whose operation is a composition of braids
x_{i}=x_{j}{\text{ for some }}i\neq j\}.} The cohomology of a group G {\displaystyle G} is defined as the cohomology of the corresponding Eilenberg–MacLane classifying
Braid_group
Russian mathematician (born 1954)
Beilinson, A.; MacPherson, R.; Schechtman, V. (1987). "Notes on Motivic Cohomology". Duke Math. J. 54 (2): 679–710. doi:10.1215/S0012-7094-87-05430-5. Beilinson
Vadim_Schechtman
German mathematician
theory of Frobenius manifolds and the explicit Künneth formula in quantum cohomology". He remained at the Max Planck Institute for one year after his graduation
Ralph_Kaufmann
Seven mathematical problems with a US$1 million prize for each solution
class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X. The official statement of the problem
Millennium_Prize_Problems
Formulation to quantize gauge field theories in physics
graded by integral ghost numbers and we have a BRST cohomology. From a practical perspective, a quantum field theory consists of an action principle and
BRST_quantization
American mathematician and professor
American Mathematical Society, 259–271. with Tamvakis, H (2003). Quantum cohomology of the Lagrangian Grassmannian. Journal of Algebraic Geometry, 12(4):777-810
Andrew_Kresch
Indian-American mathematician
over the integers. Belkale works on enumerative algebraic geometry, quantum cohomology and moduli spaces of vector bundles on curves (conformal blocks and
Prakash_Belkale
Russian mathematician
doi:10.1007/bf01453564. S2CID 119945673. Batyrev, Victor V. (1993). "Quantum cohomology rings of toric manifolds". Journées de Géométrie Algébrique d'Orsay
Victor_Batyrev
Principle in quantum field theory
In quantum field theory, the anomaly matching condition by Gerard 't Hooft states that the calculation of any chiral anomaly for the flavor symmetry must
Anomaly_matching_condition
Type of monoidal category
{\displaystyle G} and a cohomology class [ α ] ∈ H 3 ( G , U ( 1 ) ) {\displaystyle [\alpha ]\in H^{3}(G,U(1))} . On the level of topological quantum field theory
Modular_tensor_category
Context dependence in quantum measurements
Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as
Quantum_contextuality
Theoretical physicist and mathematician
Schreiber, Urs (2013). "Differential cohomology in a cohesive ∞-topos". arXiv:1310.7930v1 [math-ph]. "Center for Quantum and Topological Systems". Archived
Urs_Schreiber
French mathematician (1928–2014)
Topoi Étale cohomology and l-adic cohomology Motives and the motivic Galois group (Grothendieck ⊗-categories) Crystals and crystalline cohomology, yoga of
Alexander_Grothendieck
Italian mathematician and physicist
Hertling, Claus; Marcolli, Matilde, eds. (2003). Frobenius Manifolds: Quantum Cohomology and Singularities. Vieweg-Teubner Verlag. ISBN 978-3-322-80238-5.
Matilde_Marcolli
Topological quantum field theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type. It was discovered first by mathematical physicist Albert
Chern–Simons_theory
Awarded every year by the American Mathematical Society
1145/227683.227684. ISSN 0004-5411. Gerstenhaber, Murray (1963). "The cohomology structure of an associative ring". Annals of Mathematics. 78 (2): 267–288
Leroy_P._Steele_Prize
Mathematician
Konstanze (November 2002), "Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties", Journal of the American Mathematical Society
Konstanze_Rietsch
Formalism for Thom class representation in differential geometry
cohomology, as an equality on the level of differential forms. This has an interpretation in physics as the computation of the classical and quantum (super)
Mathai–Quillen_formalism
Area of mathematics
given by John Tate based on Galois cohomology, and also by Michael Artin and Jean-Louis Verdier based on étale cohomology. Then David Mumford (and independently
Arithmetic_topology
American mathematician
mathematical theory of quantum sheaf cohomology, Preprint 2011 With Guffin, Katz, Sharpe: Physical aspects of quantum sheaf cohomology for deformation of
Ron_Donagi
Monster and modular connection
Borcherds and Ryba reinterpreted the conjecture as a statement about Tate cohomology of a self-dual integral form of V ♮ {\displaystyle V^{\natural }} . This
Monstrous_moonshine
British-Lebanese mathematician (1929–2019)
these cohomology theories. Some of these cohomology theories, in particular complex cobordism, turned out to be some of the most powerful cohomology theories
Michael_Atiyah
Branch of mathematics
algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a cochain complex. That is, cohomology is defined as the
Algebraic_topology
Branch of mathematics
Connes, who introduced a framework in which operator algebras, cyclic cohomology and generalized differential forms could be used to study spaces that
Noncommutative_geometry
Australian mathematician
spaces. He was also a pioneer of elliptic cohomology, which is related to his interest in topological quantum field theory. Segal was an Invited Speaker
Graeme_Segal
Belgian mathematician
algebraic geometry. In joint work with George Lusztig, Deligne applied étale cohomology to construct representations of finite groups of Lie type; with Michael
Pierre_Deligne
1090/S0002-9947-1992-1043857-6. MR 1043857. Bertram Kostant (1996), "Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight ρ {\displaystyle
Hessenberg_variety
(PDF) from the original on 1 March 2020. Notes on stable maps and quantum cohomology https://amathew.wordpress.com/2012/06/02/the-stack-of-coherent-sheaves/
Quot_scheme
Mathematics award
arithmetic algebraic geometry, particularly on the development of p-adic cohomology theories." Aleksandr Logunov – "For novel techniques to study solutions
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Construction in algebra
structure on the direct sum of all homology or cohomology groups of an H-space. Locally compact quantum groups generalize Hopf algebras and carry a topology
Hopf_algebra
Branch of mathematics
most important of these invariants are homotopy groups, homology, and cohomology. Although algebraic topology primarily uses algebra to study topological
Topology
Cocycle in an entire cyclic cohomology group
Lesniewski, and Konrad Osterwalder) is a cocycle in an entire cyclic cohomology group. It is a non-commutative version of the classic Chern character
JLO_cocycle
Characteristic classes of vector bundles
form. That is, Chern classes are cohomology classes in the sense of de Rham cohomology. It can be shown that the cohomology classes of the Chern forms do
Chern_class
Theory proposed by Roger Penrose
a unification of general relativity (space-time geometry) and quantum mechanics (quantum theory) and has subsequently evolved into a widely studied branch
Twistor_theory
American mathematician (born 1937)
supersymmetric quantum field theory (mathematically, a θ-summable spectral triple) and outputs a cocycle in Alain Connes' cyclic cohomology. In his later
Arthur_Jaffe
Topological spaces whose union is a boundary
are fundamental extraordinary cohomology theories, and categories of cobordisms are the domains of topological quantum field theories. Roughly speaking
Cobordism
Topological field
theory is a topological field, which when quantized, becomes a topological quantum field theory. BF stands for background field B and F, as can be seen below
BF_model
star-multiplication characterizing quantum mechanics and underlying its uncertainty principle. Deligne's conjecture on Hochschild cohomology Poisson manifold Formality
Deformation_quantization
spaces of two-dimensional topological quantum field theories and are thereby useful in the study of quantum cohomology and Gromov–Witten invariants. 'Higher-order'
Isomonodromic_deformation
Mathematical conjecture
OCLC 794640223. Kontsevich, M.; Manin, Yu (1994). "Gromov-Witten classes, quantum cohomology, and enumerative geometry". Communications in Mathematical Physics
Mirror_symmetry_conjecture
Theory for associative algebras over rings
In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology
Hochschild_homology
Quantum capacitance Quantum cascade laser Quantum channel Quantum chaos Quantum chromodynamics Quantum cloning Quantum coherence Quantum cohomology Quantum
Index_of_physics_articles_(Q)
History of maths
using categories, including algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic and set theory in
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
American mathematician (born 1977)
fully extended topological quantum field theories; and for providing a moduli-theoretic interpretation of elliptic cohomology." Lurie was also awarded a
Jacob_Lurie
Italian mathematician (born 1949)
University of Warwick under the supervision of George Lusztig (The mod-2 cohomology of the orthogonal groups over a finite field). In 1975 he was a lecturer
Corrado_de_Concini
Theorem in the mathematical formulation of quantum mechanics
Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical symmetries such as rotations
Wigner's_theorem
American mathematician
at Chapel Hill for doctoral study, initially planning to work in quantum cohomology, but switched to functional analysis with Michael E. Taylor as her
Anna_Mazzucato
for a general field F, the Albert algebras are classified by the Galois cohomology group H1(F,G). The Kantor–Koecher–Tits construction applied to an Albert
Albert_algebra
American mathematician
[hep-th/0106099] [abs] W Pardon and M Stern, Pure hodge structure on the L2-cohomology of varieties with isolated singularities, Journal fur die Reine und Angewandte
Mark_Stern
Integral polynomial
the Weyl group of an algebraic group on ℓ {\displaystyle \ell } -adic cohomology groups related to conjugacy classes which are unipotent. They found a
Kazhdan–Lusztig_polynomial
Special tangential structure
{\displaystyle M} can be embedded in a spin manifold with two dimensions more. The cohomology ring of the infinite classifying space BSpin c := lim n → ∞ BSpin c
Spinc_structure
Topologically stable solution of a partial differential equation
having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to
Topological_defect
Algebraic geometry analog of a principal bundle in algebraic topology
1-coboundaries in cohomology; that is, the g i j {\displaystyle g_{ij}} define a cohomology class in the sheaf cohomology (more precisely Čech cohomology with sheaf
Torsor_(algebraic_geometry)
Algebra used in certain conformal field theories
ISSN 0550-3213, MR 0954762 Witten, Edward (1995), "The Verlinde algebra and the cohomology of the Grassmannian", Geometry, topology, & physics, Conf. Proc. Lecture
Verlinde_algebra
German mathematician
qualitative property of a manifold. More specifically, these should form a cohomology theory. The emerging language should be flexible enough to formulate new
Peter_Teichner
General concept and operation in mathematics
cohomology of finite, local and global fields (also known as Galois cohomology, since étale cohomology over a field is equivalent to group cohomology
Duality_(mathematics)
Australian mathematician
cohomology, as an equality on the level of differential forms. This has an interpretation in physics as the computation of the classical and quantum (super)
Varghese_Mathai
American mathematician and billionaire (1938–2024)
providing a theoretical framework to combine geometry and topology with quantum field theory. In 1994, Simons and his wife, Marilyn, founded the Simons
Jim_Simons
Irish mathematician
Costello gave a rigorous construction of the Witten genus in elliptic cohomology, using a variant of Chern–Simons theory. Along with Davide Gaiotto, Kevin
Kevin_Costello
American mathematician (born 1939)
his research interests are in homological algebra and the mathematics of quantum mechanics. He received his B.S.(1962) in Mathematics from Lincoln University
Floyd_Williams
Chinese-American physicist
(short-range entangled states with symmetry) and its description by group cohomology of the symmetry group (2011). The notion of SPT order generalizes the
Xiao-Gang_Wen
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY
QUANTUM COHOMOLOGY