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Mathematics concept
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called
Homological_mirror_symmetry
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich, and the SYZ conjecture
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Mathematical conjecture
Mirror Symmetry: The Elliptic Curve An Introduction to Homological Mirror Symmetry and the Case of Elliptic Curves Homological mirror symmetry for the
Mirror_symmetry_conjecture
Mathematician
supervision of Paul Seidel from the University of Chicago with thesis Homological Mirror Symmetry for Toric Varieties. As a postdoctoral researcher, he was a Clay
Mohammed_Abouzaid
Topics referred to by the same term
string theory Homological mirror symmetry, a mathematical conjecture about Calabi–Yau manifolds made by Maxim Kontsevich Mirror symmetry conjecture, a
Mirror symmetry (disambiguation)
Mirror_symmetry_(disambiguation)
Extended physical object in string theory
categories, and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry. The word "brane" originated in 1987
Brane
Swiss-Italian mathematician (born 1970)
December 1970) is a Swiss-Italian mathematician specializing in homological mirror symmetry. He is a faculty member at the Massachusetts Institute of Technology
Paul_Seidel
Mathematical conjecture
While the homological mirror symmetry is based on homological algebra, the SYZ conjecture is a geometrical realization of mirror symmetry. In string
SYZ_conjecture
Mathematician
Keating is a mathematician specialising in symplectic geometry and homological mirror symmetry. She is a professor in the Department of Pure Mathematics and
Ailsa_Keating
Theory of subatomic structure
understanding of mirror symmetry based on physicists' intuition. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim
String_theory
Category of a symplectic manifold
derived categories, which are the subject of the celebrated homological mirror symmetry conjecture of Maxim Kontsevich. This conjecture has now been
Fukaya_category
Symplectic topology tool
homology figures in a crucial way in the formulation of the homological mirror symmetry conjecture. In 1996 S. Piunikhin, D. Salamon and M. Schwarz summarized
Floer_homology
Category in mathematics
different origins have been proved or conjectured. For example, the homological mirror symmetry conjecture predicts that the derived category of a Calabi–Yau
Triangulated_category
French mathematician (b. 1977)
Efimov, Alexander I.; Katzarkov, Ludmil; Orlov, Dmitri (2013). "Homological mirror symmetry for punctured spheres". Journal of the American Mathematical
Denis_Auroux
theories. Toric variety Homological mirror symmetry Mirror symmetry (string theory) Batyrev, V. (1994). "Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces
Combinatorial_mirror_symmetry
Russian mathematician (born 1966)
with homological algebra, (derived categories, triangulated categories), algebraic geometry (derived algebraic geometry, homological mirror symmetry, quasicoherent
Dmitri_Olegovich_Orlov
Conjecture in symplectic geometry
which is a triangulated category appearing in Kontsevich's homological mirror symmetry conjecture. The statement of the Thomas–Yau conjecture is not
Thomas–Yau_conjecture
Russian mathematician
Gromov–Witten invariants. He is one of authors of hypothesis of homological mirror symmetry for Fano manifolds. In the theory of exponential integrals, Barannikov
Serguei_Barannikov
Algebraic structure
In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It
Mixed_Hodge_structure
Branch of mathematics that studies the properties of groups
set of symmetry operations present on it. The symmetry operation is an action, such as a rotation around an axis or a reflection through a mirror plane
Group_theory
British mathematician
Calabi-Yau 3-folds, and bundles on K3 fibrations'. Motivated by homological mirror symmetry, he produced braid group actions on derived categories of coherent
Richard Thomas (mathematician)
Richard_Thomas_(mathematician)
Skeletonized version of algebraic geometry
S2CID 250889913. Kontsevich, Maxim; Soibelman, Yan (7 November 2000). "Homological mirror symmetry and torus fibrations". arXiv:math/0011041. Mikhalkin, Grigory
Tropical_geometry
Chinese-American mathematician (born 1949)
of mirror symmetry, and research on its various aspects is currently an active field. It can be contrasted with the alternative homological mirror symmetry
Shing-Tung_Yau
American mathematician (born 1965)
Aug14Thu, 9 August 2015 on YouTube Mark Gross – Mirror symmetry, Simons Collaboration on Homological Mirror Symmetry, 26 March 2016 on YouTube "2016, C.V. Dr
Mark_Gross_(mathematician)
homotopies of homotopies, and so forth. They are ubiquitous in homological mirror symmetry because of their necessity in defining the structure of the Fukaya
Homotopy_associative_algebra
Study of vector bundles, principal bundles, and fibre bundles
to string theory and Mirror symmetry were realised, where gauge theory is essential to phrasing the homological mirror symmetry conjecture and the AdS/CFT
Gauge_theory_(mathematics)
British mathematician (born 1973)
1938, Springer, 2008, 1–53, Arxiv with Mohammed Abouzaid: "Homological mirror symmetry for the 4-torus", Duke Math. J., Vol. 152, 2010, pp. 373–440
Ivan_Smith_(mathematician)
Russian mathematician
collaboration with Maxim Kontsevich is devoted to various aspects of homological mirror symmetry, a proof of Deligne conjecture about operations on the cohomological
Yan_Soibelman
International science award since 2012
Bures-sur-Yvette Numerous contributions including development of homological mirror symmetry, and the study of wall-crossing phenomena. Andrei Linde Stanford
Breakthrough Prize in Fundamental Physics
Breakthrough_Prize_in_Fundamental_Physics
History of maths
algebraic structures including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories, including algebraic
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
describing these branes. In the B-model of topological string theory, homological mirror symmetry suggests D-branes should be viewed as elements of the derived
Deformed Hermitian Yang–Mills equation
Deformed_Hermitian_Yang–Mills_equation
Japanese mathematician
submanifolds and its implications in symplectic geometry and homological mirror symmetry. Ono was awarded by the Mathematical Society of Japan in 1999
Kaoru_Ono
Homological construction
derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory
Derived_category
Field of knowledge
Mathematically, the symmetries of an object form a group known as the symmetry group. For example, the group underlying mirror symmetry is the cyclic group
Mathematics
Mathematics timeline
and Seiberg–Witten theory. 1994 Maxim Kontsevich Formulates homological mirror symmetry conjecture: X a compact symplectic manifold with first chern
Timeline_of_manifolds
English mathematics professor (born 1973)
geometry. It has been a central component of subsequent work on homological mirror symmetry. Bridgeland's research has been funded by the Engineering and
Tom_Bridgeland
Mathematics study in geometry
decomposition Fourier–Mukai transform Bridgeland stability condition Homological mirror symmetry Shklyarov, D. (2013). "Hirzebruch-Riemann-Roch-type formula for
Derived noncommutative algebraic geometry
Derived_noncommutative_algebraic_geometry
Theory in physics
the Kähler moduli space of a Calabi-Yau manifold, as considered in mirror symmetry, and the resulting subcategory P ⊂ D b ( M ) {\displaystyle {\mathcal
Donaldson–Thomas_theory
Periodic spatial graph
realized by a symmetry. However, the overall structure is chiral: no sequence of translations and rotations can make it coincide with its mirror image. The
Laves_graph
Russian mathematician (1937–2023)
Sergei (1994). Homological algebra. Encyclopedia of Mathematical Sciences. Springer. Manin, Yuri; Gelfand, Sergei (1996). Methods of Homological algebra. Springer
Yuri_Manin
Branch of mathematics
complex variables, and has found applications to string theory and mirror symmetry. Complex geometry first appeared as a distinct area of study in the
Geometry
Construct in mathematics
In mathematics, a gerbe (/dʒɜːrb/; French: [ʒɛʁb]) is a construct in homological algebra and topology. Gerbes were introduced by Jean Giraud (Giraud 1971)
Gerbe
Algebraic structure in homological algebra
In mathematics – particularly in homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra)
Differential_graded_algebra
Algebraic structure
their Methods of homological algebra, that unlike Galois symmetries acting on other cohomology groups, the origin of "Hodge symmetries" is very mysterious
Hodge_structure
Objects of certain abelian categories associated to topological spaces
this ground state variety in all dimensions, found it compatible with Mirror symmetry and String Theory but found an obstruction in the middle dimension
Perverse_sheaf
Awarded every year by the American Mathematical Society
to much current research activity, including quantum cohomology and mirror symmetry. 1996 Daniel Stroock and S. R. Srinivasa Varadhan for their four papers
Leroy_P._Steele_Prize
Mathematics award
Seidel, and other decisive contributions to symplectic topology and mirror symmetry." 2018 Zhiwei Yun – "For deep work on the global Gan-Gross-Prasad conjecture
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Branch of mathematics
Tony Pantev, Hodge theoretic aspects of mirror symmetry, arxiv/0806.0107 Dmitri Kaledin, Tokyo lectures "Homological methods in non-commutative geometry"
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
and René Thom. Braid groups are linear Ruth Lawrence's 1990 paper, "Homological representations of the Hecke algebra", in Communications in Mathematical
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
General concept and operation in mathematics
Matlis duality Petrie duality Pontryagin duality S-duality T-duality, Mirror symmetry Atiyah 2007, p. 1 Kostrikin 2001, This quote is the first sentence
Duality_(mathematics)
coloring Claire Voisin (born 1962), French expert on Hodge structures and mirror symmetry, member of French Academy of Sciences Elisabeth Vreede (1879–1943)
List_of_women_in_mathematics
Manifold with Riemannian, complex and symplectic structure
numbers of a compact Kähler manifold satisfy several identities. The Hodge symmetry h p , q = h q , p {\displaystyle h^{p,q}=h^{q,p}} holds because the Laplacian
Kähler_manifold
Interplay between observation, experiment, and theory in science
characteristic) into or out of forms from homology, or more abstractly, from homological algebra. Lakatos proposed an account of mathematical knowledge based
Scientific_method
American annual mathematics conference
calibration C.-N. Yang, Vector potentials and connections Shing-Tung Yau, Mirror symmetry and rational curves Peter Sarnak, Some spectral problems on negatively
Geometry_Festival
Branch of mathematics
Springer. ISBN 978-3-540-72185-7. Cox, David A.; Katz, Sheldon (1999). Mirror Symmetry and Algebraic Geometry. American Mathematical Soc. ISBN 978-0-8218-2127-5
Algebraic_geometry
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HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
HOMOLOGICAL MIRROR-SYMMETRY
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