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Branch of algebraic geometry concerned with counting solutions
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by
Enumerative_geometry
Branch of algebraic geometry
problems of projective geometry and, as such, is viewed as part of enumerative geometry. Giving it a more rigorous foundation was the aim of Hilbert's 15th
Schubert_calculus
Theory of subatomic structure
problems in enumerative geometry, a branch of mathematics concerned with counting the numbers of solutions to geometric questions. Enumerative geometry studies
String_theory
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
particular, the enumerative predictions of mirror symmetry have now been rigorously proven. In addition to its applications in enumerative geometry, mirror symmetry
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
definition of invariants of spectral curves. It has applications in enumerative geometry, random matrix theory, mathematical physics, string theory, knot
Topological_recursion
Canadian-American mathematician
and his research work spans over enumerative geometry, topology, Gromov–Witten theory, and classical algebraic geometry. He has solved several old problems
Ravi_Vakil
Study of complex manifolds and several complex variables
advances in enumerative geometry of complex varieties. The Hodge conjecture, one of the millennium prize problems, is a problem in complex geometry. Broadly
Complex_geometry
Chinese-American mathematician (born 1949)
mathematical and physical fields of convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while
Shing-Tung_Yau
Overview of and topical guide to geometry
Elliptic geometry Enumerative geometry Epipolar geometry Euclidean geometry Finite geometry Fractal geometry Geometry of numbers Hyperbolic geometry Incidence
Outline_of_geometry
Danish mathematician (1839–1920)
January 1920) was a Danish mathematician. He is known for work on the enumerative geometry of conic sections, algebraic surfaces, and history of mathematics
Hieronymus_Georg_Zeuthen
Type of geometry
projective geometry became less fashionable, although the literature is voluminous. Some important work was done in enumerative geometry in particular
Projective_geometry
In enumerative geometry, Steiner's conic problem is the problem of finding the number of smooth conics tangent to five given conics in the plane in general
Steiner's_conic_problem
space. Enumerative combinatorics an area of combinatorics that deals with the number of ways that certain patterns can be formed. Enumerative geometry a branch
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
23 mathematical problems stated in 1900
in Hamburg 1 (1886), 134-155. S. Kleiman, Intersection theory and enumerative geometry: A decade in review, Proc. Symp. Pure Math., 46:2, Amer. Math. Soc
Hilbert's_problems
American mathematician
American mathematician at the University of Michigan. He works in enumerative geometry, and is also known for his chess playing, where he is a FIDE Master
Aaron_Pixton
German mathematician
Schubert was one of the leading developers of enumerative geometry, which considers those parts of algebraic geometry that involve a finite number of solutions
Hermann_Schubert
Italian mathematician and academic
Her research includes work in algebraic geometry, arithmetic geometry, tropical geometry and enumerative geometry. Caporaso earned a laurea from Sapienza
Lucia_Caporaso
Study of systems of inequalitites
ISBN 978-3-7643-8309-1. Zbl 1162.14300. Mikhalkin, Grigory (2005). "Enumerative tropical algebraic geometry in R 2 {\displaystyle \mathbb {R} ^{2}} ". Journal of the
Real_algebraic_geometry
Principle in geometry
enumerative geometry; formalizing this intuition requires significant further development to justify. Another classic problem in enumerative geometry
Five_points_determine_a_conic
Application of homotopy to algebraic varieties
Bloch-Kato conjectures. It has also recently revolutionized the theory of enumerative geometry problems. A1 homotopy theory is founded on a category called the
A¹_homotopy_theory
Branch of mathematics
Marcos Marino; Michael Thaddeus; Ravi Vakil (2008). Enumerative Invariants in Algebraic Geometry and String Theory: Lectures given at the C.I.M.E. Summer
Geometry
On Schubert's enumerative calculus
intersection theory of the 19th century, together with applications to enumerative geometry. Justifying this calculus was the content of Hilbert's 15th problem
Hilbert's_fifteenth_problem
American mathematician (born 1956)
2006). "Review: Enumerative Geometry and String Theory by Sheldon Katz". Mathematical Association of America. "Review: Enumerative Geometry and String Theory"
Sheldon_Katz
3d hypersurface of degree 5
these agree with the actual number of points. Deformation theory Enumerative geometry Gromov–Witten invariant Hodge structure Jacobian ideal - gives an
Quintic_threefold
Object in algebraic geometry
curve is a type of stack used in studying Gromov–Witten theory, enumerative geometry, and rings of modular forms. Stacky curves are closely related to
Stacky_curve
Branch of discrete mathematics
combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic side, besides
Combinatorics
French mathematician (1793–1880)
characteristics that enabled the correct enumeration of the conics (there are 3264) (see enumerative geometry). He established several important theorems
Michel_Chasles
Mathematics award
spaces" 2013 Rahul Pandharipande "For his recent outstanding work in enumerative geometry, specifically for his proof in a large class of cases of the MNOP
Clay_Research_Award
Skeletonized version of algebraic geometry
definitions of the theory. This was motivated by its application to enumerative algebraic geometry, with ideas from Maxim Kontsevich and works by Grigory Mikhalkin
Tropical_geometry
Branch of algebraic geometry
Grothendieck–Riemann–Roch theorem Enumerative geometry Eisenbud & Harris 2016, p. 14. Eisenbud & Harris 2016, p. 2. Gathman, Andreas, Algebraic Geometry, archived from the
Intersection_theory
Type of object in algebraic geometry
points are Deligne–Mumford stacks, and their geometry plays a central role in modern enumerative geometry and intersection theory. A stacky curve is, roughly
Deligne–Mumford_stack
Mathematician
Vasileva Georgieva is a mathematician whose research interests include enumerative geometry, symplectic topology, and Gromov–Witten invariants. Educated in Bulgaria
Penka_Georgieva
American annual mathematics conference
eigenfunctions Jim Bryan (University of British Columbia) AG - The enumerative geometry and arithmetic of some of the world’s Tiniest Calabi–Yau threefolds
Geometry_Festival
Concept in algebraic geometry
Gromov–Witten invariants, quantum cohomology has important implications for enumerative geometry. It also connects to many ideas in mathematical physics and mirror
Quantum_cohomology
One of eight divisions of a Euclidean 3D coordinate system
An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It
Octant_(solid_geometry)
the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem
Vertex_enumeration_problem
Generating function in integrable systems
sense of combinatorics and enumerative geometry, especially in relation to moduli spaces of Riemann surfaces, and enumeration of branched coverings, or
Tau function (integrable systems)
Tau_function_(integrable_systems)
Equivalence of two physical theories
has important applications in a branch of mathematics called enumerative algebraic geometry. T-duality is a particular example of a general notion of duality
T-duality
calculate the Gromov–Witten invariants, which find application in enumerative geometry and type IIA string theory. The idea of stable maps was proposed
Stable_map
19th century French mathematician
for his work in geometry, particularly in enumerative geometry and the singularity theory of algebraic curves, in algebraic geometry. He also worked on
Georges_Henri_Halphen
Theory in physics
of integer valued invariants, one considers motivic invariants. Enumerative geometry Gromov–Witten invariant Hilbert scheme Quantum cohomology Bridgeland
Donaldson–Thomas_theory
Michael; Tate, John (eds.), "Towards an Enumerative Geometry of the Moduli Space of Curves", Arithmetic and Geometry: Papers Dedicated to I.R. Shafarevich
Moduli_of_abelian_varieties
Analogs of homology groups for algebraic varieties
intersection; this is a version of Bézout's theorem, a classic result of enumerative geometry. Given a vector bundle E → X {\displaystyle E\to X} of rank r {\displaystyle
Chow_group
Chinese-American mathematician
collaboration with Bong Lian and Shing-Tung Yau in which they establish some enumerative geometry conjectures motivated by mirror symmetry. Liu was born in Kaifeng
Kefeng_Liu
Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor
Mathematical Society, ISBN 978-1-4704-4188-3 Bott's formula and enumerative geometry The Number of Twisted Cubics on a Quintic Threefold Rational curves
Hilbert_scheme
American mathematician
ISBN 0-8218-1198-3, 81-06 (81T30 81Txx) Quantum field theory, supersymmetry, and enumerative geometry. Freed, Daniel S. and Morrison, David R. and Singer, Isadore editors
Dan_Freed
Algebraic surface defined by a cubic polynomial
Lerario, A.; Lundberg, E.; Peterson, C. (2019). "Random fields and the enumerative geometry of lines on real and complex hypersurfaces". Mathematische Annalen
Cubic_surface
Study of discrete mathematical structures
mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has
Discrete_mathematics
Result in algebraic geometry
Mumford, David (1983). "Towards an Enumerative Geometry of the Moduli Space of Curves". Arithmetic and Geometry. pp. 271–328. doi:10.1007/978-1-4757-9286-7_12
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
Italian-American mathematician
ring of integers. Aluffi’s research is in algebraic geometry. Most of it deals with enumerative geometry and with singularity theory, specifically characteristic
Paolo_Aluffi
Concept in string theory
projective varieties can be defined entirely within algebraic geometry. The classical enumerative geometry of plane curves and of rational curves in homogeneous
Gromov–Witten_invariant
Construct in algebraic geometry
curves with n {\displaystyle n} punctures to a fixed target. Since enumerative geometry studies the generic behavior of such maps, the deformation theory
Cotangent_complex
operations research to organ transplants Penka Georgieva, expert on enumerative geometry, symplectic topology, and Gromov–Witten invariants Maria-Pia Geppert
List_of_women_in_mathematics
Mathematical space
affine subpaces called Schubert cells, which were first applied in enumerative geometry. The Schubert cells for G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)}
Grassmannian
computations in enumerative geometry". p. 13. arXiv:1512.07363 [math.AG]. N. Chris and V. Ginzburg, Representation Theory and Complex Geometry, Birkhäuser
Equivariant algebraic K-theory
Equivariant_algebraic_K-theory
Mathematical physicist
mathematics, including knot theory (refined Chern–Simons theory),[3] enumerative geometry,[2] mirror symmetry,[1][4] and the geometric Langlands correspondence
Mina_Aganagić
Stability conditions for triangulated cateogires
in the stability manifold, has been employed to solve problems in enumerative geometry and Brill-Noether theory. To construct well-behaved moduli spaces
Bridgeland stability condition
Bridgeland_stability_condition
Mathematical conjecture
this way enumerative geometry becomes important for understanding how mirror symmetry interchanges dual objects. By combining the geometry of mirror
SYZ_conjecture
Ordered listing of items in collection
(perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term enumeration is used more in the sense of counting – with emphasis
Enumeration
Method of logical reasoning
used to reach inductive generalizations are enumerative induction and eliminative induction. Enumerative induction is an inductive method in which a generalization
Inductive_reasoning
and continued by Zeuthen in the 19th century under the heading of enumerative geometry. This area was deemed by David Hilbert important enough to be included
Schubert_variety
Application of geometry in number theory
Geometry of numbers, also known as geometric number theory, is the part of number theory which uses geometry for the study of algebraic numbers. Typically
Geometry_of_numbers
Rational numbers with root 5 added
Gustav Lejeune Dirichlet and Adrien-Marie Legendre in 1825–1830. In enumerative geometry, it is proven that every non-singular cubic surface contains exactly
Golden_field
Maxim; Manin, Yuri. "Gromov-Witten Classes, Quantum Cohomology, and Enumerative Geometry" (PDF). p. 9. Archived (PDF) from the original on 2009-11-28. Fulton
Convexity (algebraic geometry)
Convexity_(algebraic_geometry)
Vector bundles theorem
one sense in which the correspondence has had lasting impacts in enumerative geometry. Kobayashi, Shoshichi (1982). "Curvature and stability of vector
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
In mathematics, specifically enumerative geometry and symplectic geometry, the virtual fundamental class [ X ] vir ∈ H ∗ ( X ) {\displaystyle [X]^{\text{vir}}\in
Virtual_fundamental_class
Geometry problem about finding touching circles
different types of Apollonius's problem belongs to the field of enumerative geometry. The general number of solutions for each of the ten types of Apollonius's
Problem_of_Apollonius
Roman-era temple to Mithra in Jajce, Bosnia and Herzegovina
([0-9a-fA-F]{3}){1,2}$ /0/geometries: The property geometries is required /0/type: Does not have a value in the enumeration ["GeometryCollection"] /0/type:
Jajce_Mithraeum
Field of knowledge
properties), algebra (the study of operations and the structures they form), geometry (the study of shapes and spaces that contain them), analysis (the study
Mathematics
Mathematical logic concept
theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable,
Computably_enumerable_set
Intermodal transit station in Jacksonville, Florida, United States
property geometries is required /0/type: Does not have a value in the enumeration ["GeometryCollection"] /0/type: Does not have a value in the enumeration ["MultiPolygon"]
Jacksonville Regional Transportation Center at LaVilla
Jacksonville_Regional_Transportation_Center_at_LaVilla
Mathematics timeline
calculus in several variables, mathematical analysis and differential geometry; piecewise-linear manifolds; topological manifolds. There are also related
Timeline_of_manifolds
Problem in algebraic geometry
enumerative geometry (e.g., Steiner's conic problem) and the derivation of the multiple-point formula, the formula allowing one to count or enumerate
Residual_intersection
Area of combinatorics
combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic side, besides
Algebraic_combinatorics
Type of incidence structure
(1984), "Strongly regular graphs and partial geometries", in Jackson, D.M.; Vanstone, S.A. (eds.), Enumeration and Design, Toronto: Academic Press, pp. 85–122
Partial_geometry
List of numerical computational geometry topics enumerates the topics of computational geometry that deals with geometric objects as continuous entities
List of numerical computational geometry topics
List_of_numerical_computational_geometry_topics
American mathematician
undergraduate, and earned her Ph.D. at MIT in 1983. Her dissertation, On the Enumerative Geometry of Stationary Multiple-points, was supervised by Steven Kleiman.
Susan_Jane_Colley
American mathematician
the lines on a smooth cubic surface, generalizing known results in enumerative geometry, and stimulating new research in the field. Wickelgren was named
Kirsten_Wickelgren
Professor of mathematics (born 1969)
Technology Zürich (ETH) working in algebraic geometry. His particular interests concern moduli spaces, enumerative invariants associated to moduli spaces,
Rahul_Pandharipande
American mathematician
algebraic geometry and commutative algebra. He has made seminal contributions in motivic cohomology, moduli theory, intersection theory and enumerative geometry
Steven_Kleiman
Mathematics textbook
Itenberg et al., some topics in tropical geometry are (deliberately) omitted, including enumerative geometry and mirror symmetry. The book has six chapters
Introduction to Tropical Geometry
Introduction_to_Tropical_Geometry
colleagues show that mirror symmetry could be used to solve problems in enumerative geometry. Qiudong Wang produces a global solution to the n-body problem. January
1991_in_science
Mathematical description of spacetime used in relativity
-1/R^{2}} . The 1 in the upper index refers to an enumeration of the different model spaces of hyperbolic geometry, and the n for its dimension. A 2 ( 2 ) {\displaystyle
Minkowski_spacetime
(1998). It recovers some classical results from Schubert's book on enumerative geometry. Viewing the dual projective space P 3 ˘ {\displaystyle {\breve {\mathbb
Segre_class
Solid made by joining an n- and 2n-gon with triangles and pentagons
In geometry, a rotunda is any member of a family of cyclic-symmetric polyhedra. They are similar to a cupola but, instead of alternating squares and triangles
Rotunda_(geometry)
Tiling of euclidean or hyperbolic space of three or more dimensions
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of
Honeycomb_(geometry)
Public school in Vestal, New York
Illinois at Urbana–Champaign Aaron Pixton 2004 Mathematician at the University of Michigan specializing in enumerative geometry; 3 time Putnam Fellow
Vestal_High_School
Unicameral legislature of the Indonesian province of North Sumatra
service is required /0/geometries: The property geometries is required /0/type: Does not have a value in the enumeration ["GeometryCollection"] /0/type:
North Sumatra Regional House of Representatives
North_Sumatra_Regional_House_of_Representatives
Basis for Euclidean geometry
Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those
Hilbert's_axioms
Geometric object with flat sides
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any
Polytope
List of combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
American mathematician
Superconformal Field Theories). Quantum field theory, supersymmetry, and enumerative geometry. Freed, Daniel S. and Morrison, David R. and Singer, Isadore editors
David R. Morrison (mathematician)
David_R._Morrison_(mathematician)
Academic conference
combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal
Eurocomb
Topological space that locally resembles Euclidean space
projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures
Manifold
Italian mathematician (born 1941)
invariant theory, enumerative geometry, infinite dimensional algebras and quantum groups, polytopes, braid groups, cyclic homology, geometry of orbits of compact
Claudio_Procesi
Italian partisan and spy (1918–2022)
with geometric applications) with Alexandru T. Lascu, A formula of enumerative geometry To hide from the Nazi-Fascists, Fiorentini changed identity several
Mario_Fiorentini
Station of the Jacksonville Skyway
property geometries is required /0/type: Does not have a value in the enumeration ["GeometryCollection"] /0/type: Does not have a value in the enumeration ["MultiPolygon"]
Jefferson station (Jacksonville)
Jefferson_station_(Jacksonville)
Aspects include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing
Lists_of_mathematics_topics
Jacksonville Skyway monorail station in Florida, United States
property geometries is required /0/type: Does not have a value in the enumeration ["GeometryCollection"] /0/type: Does not have a value in the enumeration ["MultiPolygon"]
Riverplace_station
Geometry definition file format
OBJ (or .OBJ) is a geometry definition file format first developed by Wavefront Technologies for The Advanced Visualizer animation package. It is an open
Wavefront_.obj_file
ENUMERATIVE GEOMETRY
ENUMERATIVE GEOMETRY
Girl/Female
Biblical
Image, figure, enumeration.
Boy/Male
Greek
Greek surname. Euclid was an early developer of geometry theories.
Biblical
image; figure; enumeration
ENUMERATIVE GEOMETRY
ENUMERATIVE GEOMETRY
Boy/Male
Indian
Knowledgeable Man
Boy/Male
Hindu, Indian
Meaning of Intention
Boy/Male
Hindu, Indian
Carry-on; Joyful; Lamb
Boy/Male
Muslim
Sharp-minded, Wise
Surname or Lastname
English
English : from the Old English byname Topp meaning ‘tuft’, ‘crest’, or the cognate Old Norse Toppr.German : from Low German topp ‘point’, ‘tree top’, hence a topographic name; or alternatively a metonymic occupational name or nickname from the same word in the sense ‘braid’.German : variant of Dopp.Jewish (Ashkenazic) : variant spelling of Top.
Girl/Female
Hindu
Belonging to one, Striving for the absolute
Girl/Female
Tamil
Beautifully drawn
Boy/Male
Bengali, Hindu, Indian
By Blessing of the God Shiva
Girl/Female
Bengali, Indian, Telugu
Honest; The Best One; Marigold
Surname or Lastname
English
English : unexplained.Possibly an Americanized spelling of French Imbert or a translation of German and Jewish Bernstein, which means ‘amber’.Muslim (widespread throughout the Muslim world) : from the Arabic personal name ‛Anbar, literally ‘perfume’, ‘ambergris’, figuratively ‘good’, ‘pleasant’, ‘agreeable’.
ENUMERATIVE GEOMETRY
ENUMERATIVE GEOMETRY
ENUMERATIVE GEOMETRY
ENUMERATIVE GEOMETRY
ENUMERATIVE GEOMETRY
n.
Enumeration.
v. i.
To sum up, or enumerate by heads or topics, what has been previously said; to repeat briefly the substance.
a.
Too numerous or variable to make a particular enumeration important; -- said of the parts of a flower, and the like. Also, indeterminate.
a.
Of or pertaining to numeration; as, a numerative system.
v. i.
To make an enumeration or computation; to engage in numbering or computing.
p. pr. & vb. n.
of Enumerate
n.
The act of reviewing or revising; review; examination; enumeration.
n.
A reckoning; computation; calculation; enumeration; a record of some reckoning; as, the Julian account of time.
v. t.
To count; to tell by numbers; to count over, or tell off one after another; to number; to reckon up; to mention one by one; to name over; to make a special and separate account of; to recount; as, to enumerate the stars in a constellation.
n.
The act of enumerating, making separate mention, or recounting.
n.
To count; to reckon; to ascertain the units of; to enumerate.
n.
A recapitulation, in the peroration, of the heads of an argument.
imp. & p. p.
of Enumerate
a.
Counting, or reckoning up, one by one.
n.
Enumeration; computation.
n.
Enumeration; mention; as, a citation of facts.
v. t.
To count; to enumerate; to number; also, to compute; to calculate.
v. t.
To keep account of; to enumerate and register; as, to mark the points in a game of billiards or cards.
n.
A detailed account, in which each thing is specially noticed.
n.
Enumeration of parts or particulars.