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Field in mathematics
Spectral geometry is a field in mathematics which concerns relationships between geometric structures of domains and manifolds and spectra of canonically
Spectral_geometry
Theorem in analysis
another, as can be seen from the account given below in terms of spectral geometry. They can also all be regarded as special cases of various forms of
Wirtinger's inequality for functions
Wirtinger's_inequality_for_functions
Chinese-American mathematician (born 1949)
are a conjecture on existence of minimal hypersurfaces and on the spectral geometry of minimal hypersurfaces. In 1978, by studying the complex Monge–Ampère
Shing-Tung_Yau
Branch of mathematics
definition agrees. Another theory of derived algebraic geometry is encapsulated by the theory of spectral schemes. Their definition requires a fair amount of
Derived_algebraic_geometry
French mathematician
Laura Monk is a French mathematician whose research in spectral geometry, on the expansion and spectral properties of random hyperbolic surfaces, continues
Laura_Monk
American mathematician (1952–2002)
mathematician known for his work in spectral geometry, Riemann surfaces, circle packings, and differential geometry. Brooks was born in 1952 in Washington
Robert_W._Brooks
Branch of mathematics
algebraic geometry Noncommutative torus Noncommutative topology Phase space formulation Quasi-free algebra Spectral action principle Spectral triple Connes
Noncommutative_geometry
Collection of mathematical theories
theory Compact operators, Isospectral operators, Completeness Spectral geometry Spectral graph theory List of functional analysis topics Jean Alexandre
Spectral_theory
Linear algebra aspects of graph theory
Brief Introduction to Spectral Graph Theory". Zurich: EMS Press. ISBN 978-3-03719-188-0. Pavel Kurasov (2024), Spectral Geometry of Graphs, Springer(Birkhauser)
Spectral_graph_theory
Number of available physical states per energy unit
Adachi T. and Sunada. T (1993). "Density of states in spectral geometry of states in spectral geometry". Comment. Math. Helv. 68: 480–493. doi:10.1007/BF02565831
Density_of_states
Mathematics award
Yaiza Canzani (2022), "in recognition of outstanding contributions in spectral geometry and microlocal analysis". Robin Neumayer (2024), for "outstanding
Sadosky_Prize
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric
Spectral_triple
Tool in homological algebra
algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization
Spectral_sequence
Mathematical theorem about the real analytic Eisenstein series
at this pole. This formula has an interpretation in terms of the spectral geometry of the elliptic curve E τ {\displaystyle E_{\tau }} associated to
Kronecker_limit_formula
theory, it is a subset of synthetic differential geometry. Solid geometry Spatial geometry Spectral geometry a field that concerns the relationships between
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Mathematical concept
(graph theory) Cheeger constant (Riemannian geometry) Eigengap Spectral gap (physics) Spectral radius Spectral gap conjecture "Impossible-Seeming Surfaces
Spectral_gap
curve singularities" in Geometry and Topology of Caustics. Polish Academy of Sciences. 2006. pp. 86–91. Majid Gazor, Pei Yu, "Spectral sequences and parametric
Arnold's_spectral_sequence
Spanish and Uruguayan mathematician
known for her work in mathematical analysis, and particularly in spectral geometry and microlocal analysis. She is an associate professor of mathematics
Yaiza_Canzani
Mathematical theorem
The trace formula has applications to arithmetic geometry, analytic number theory, spectral geometry, and the theory of automorphic forms. In the case
Selberg_trace_formula
Polish-American Mathematician (1914–1984)
off research into spectral geometry, the idea of understanding the extent to which the spectrum allows one to read back the geometry. In the end, the answer
Mark_Kac
Iranian mathematician
mathematician whose research concerns geometric analysis, spectral geometry, and differential geometry. She is a lecturer in pure mathematics in the School
Asma_Hassannezhad
Fursaev, Dmitri; Vassilevich, Dmitri (2011), Operators, Geometry and Quanta: Methods of Spectral Geometry in Quantum Field Theory, Theoretical and Mathematical
Zeta_function_(operator)
Spectral Geometry Phenomenon
In spectral geometry, the Rayleigh–Faber–Krahn inequality, named after its conjecturer, Lord Rayleigh, and the two individuals who independently proved
Rayleigh–Faber–Krahn inequality
Rayleigh–Faber–Krahn_inequality
EMS Press Cheeger, Jeff (1983), "Spectral geometry of singular Riemannian spaces", Journal of Differential Geometry, 18 (4): 575–657, doi:10.4310/jdg/1214438175
L²_cohomology
Japanese mathematician (born 1948)
Education Society of Japan. Sunada's work covers complex analytic geometry, spectral geometry, dynamical systems, probability, graph theory, discrete geometric
Toshikazu_Sunada
French mathematician
is now a Professor at Université de Strasbourg and holder of the Spectral Geometry chair at the Collège de France. In 2012 she was one of four recipients
Nalini_Anantharaman
Gilkey, Peter B.; Leahy, John V.; Park, Jeonghyeong (1998), Spinors, Spectral Geometry, and Riemannian Submersions, Global Analysis Research Center, Seoul
Riemannian_submersion
Type of mathematical function
representation – Concept in mathematics Rayleigh–Faber–Krahn inequality – Spectral Geometry Phenomenon Riesz rearrangement inequality Sobolev space – Vector space
Symmetric decreasing rearrangement
Symmetric_decreasing_rearrangement
Branch of mathematics
manifolds. Global questions of Riemannian geometry are often studied. One example is the spectral geometry of the Laplace–Beltrami operator, which generalizes
Mathematical_analysis
Principles of algebraic geometry Deligne, P. (1968). "Théorème de Lefschetz et Critères de Dégénérescence de Suites Spectrales". Publications Mathématiques
Hodge–de Rham spectral sequence
Hodge–de_Rham_spectral_sequence
American mathematician
Atiyah-Singer-Index theorem. Publish or Perish. 1984. Online Asymptotic formulae in spectral geometry. Studies in Advanced Mathematics. Vol. 43. Boca Raton, Florida: Chapman
Peter_B._Gilkey
Mathematical problem in spectral theory
condition, such as the Neumann boundary condition, can be imposed. See spectral geometry and isospectral as related articles. In 1964, John Milnor observed
Hearing_the_shape_of_a_drum
Romanian-American mathematician
geometric analysis (including topology of infinite dimensional manifolds, spectral geometry, dynamical systems), and applied topology (including computational
Dan_Burghelea
Type of geometric quantity
The spectral dimension is a real-valued quantity that characterizes a spacetime geometry and topology. It characterizes a spread into space over time,
Spectral_dimension
French mathematician
differential geometry. He is particularly known for his introduction of Gauduchon metrics in hermitian geometry. His textbook on spectral geometry, written
Paul_Gauduchon
Fundamental theorem in probability theory and statistics
Gaposhkin (1966), Sect. 1.5. Kotani, M.; Sunada, Toshikazu (2003). Spectral geometry of crystal lattices. Vol. 338. Contemporary Math. pp. 271–305.
Central_limit_theorem
Process forming a path from many random steps
the Royal Society Interface, 2008 Kotani, M.; Sunada, T. (2003). Spectral geometry of crystal lattices. Contemporary Mathematics. Vol. 338. pp. 271–305
Random_walk
Fundamental theorem in condensed matter physics
in terms of unitary characters of a lattice group, and applied to spectral geometry. Floquet theory is usually not done in a Hilbert space of functions
Bloch's_theorem
American mathematician
and her Ph.D. from Stanford University in 2006. Her dissertation, Spectral Geometry and Asymptotically Conic Convergence, was supervised by Rafe Mazzeo
Julie_Rowlett
Class of methods used in numerical analysis and scientific computing to solve ODE/PDE
Fourier series methods for periodic geometry problems, polynomial spectral methods for finite and unbounded geometry problems, pseudospectral methods for
Spectral_method
Spectral sequence
{\displaystyle G} . Many spectral sequences in algebraic geometry are instances of the Grothendieck spectral sequence, for example the Leray spectral sequence. If
Grothendieck spectral sequence
Grothendieck_spectral_sequence
Partial differential equation describing the evolution of temperature in a region
closely related with spectral geometry. A seminal nonlinear variant of the heat equation was introduced to differential geometry by James Eells and Joseph
Heat_equation
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Modes of vibration in mathematics
u satisfying the Dirichlet boundary condition. More generally, in spectral geometry one considers (1) on a manifold with boundary Ω. Then Δ is taken to
Dirichlet_eigenvalue
In symplectic geometry, the spectral invariants are invariants defined for the group of Hamiltonian diffeomorphisms of a symplectic manifold, which is
Spectral_invariants
1007/s002200050033, S2CID 121065949 Kotani, M.; Sunada, T. (2003), "Spectral geometry of crystal lattices", Heat Kernels and Analysis on Manifolds, Graphs
Periodic_graph_(geometry)
Quillen), is a spectral sequence converging to the sheaf cohomology of a type of topological space that occurs in algebraic geometry. It is used in calculating
Quillen_spectral_sequence
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
Linear operators with a common spectrum
coincide. One of fundamental problems in spectral geometry is to ask to what extent the eigenvalues determine the geometry of a given manifold. There are many
Isospectral
useful choices for u. Applications include eigenvalue estimates in spectral geometry and the study of submanifolds of constant mean curvature. Reilly 1977
Reilly_formula
French mathematician
(2012). Progress in Inverse Spectral Geometry. Birkhäuser. p. 137. ISBN 9783034889384. Brooks, Robert (2005). Geometry, Spectral Theory, Groups, and Dynamics
Marie-France_Vignéras
Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes
Spectral_shape_analysis
symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry (over
Glossary of symplectic geometry
Glossary_of_symplectic_geometry
Mathematics prize
McDuff was the first recipient of the award, for her work on symplectic geometry. A joint award was given for the first time in 2001, when Karen E. Smith
Ruth Lyttle Satter Prize in Mathematics
Ruth_Lyttle_Satter_Prize_in_Mathematics
Award given by London Mathematical Society
mathematicians". 2022 Asma Hassannezhad, "for her outstanding work in spectral geometry and her substantial contributions toward the advancement of women
Anne_Bennett_Prize
Topics referred to by the same term
Krahn (1896–1977), German actress Rayleigh–Faber–Krahn inequality, in spectral geometry Kraan (disambiguation) Kran (disambiguation) All pages with titles
Krahn_(disambiguation)
Canzani, Spanish and Uruguayan mathematical analysis, known for work in spectral geometry and microlocal analysis Mireille Capitaine, French researcher on random
List_of_women_in_mathematics
alumni, mathematician who contributed to various fields in geometry, including spectral geometry, Reinhardt domain, Ihara zeta function, and periodic graph)[citation
List of Tokyo Institute of Technology people
List_of_Tokyo_Institute_of_Technology_people
Index of articles associated with the same name
occur in fields such as calculus, differential equations and Riemannian geometry. In the theory of differential equations, comparison theorems assert particular
Comparison_theorem
American mathematician
study of differential equations on varying topological spaces, and spectral geometry, the study of these spaces through the systems of fundamental solutions
Mary_Sandoval
Greek mathematician (born 1951)
M. Craioveanu, M. Puta and Th.M. Rassias, Old and New Aspects in Spectral Geometry, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001. P. Enflo
Themistocles_M._Rassias
non-commutative Standard Model (best known as Spectral Standard Model), is a model based on noncommutative geometry that unifies a modified form of general
Noncommutative_standard_model
Romanian mathematician (1950–2007)
Mircea; Rassias, Themistocles M. (2001). Old and new aspects in spectral geometry. Mathematics and its Applications. Vol. 534. Dordrecht: Kluwer Academic
Mircea_Puta
Cocycle in an entire cyclic cohomology group
structure of non-commutative differential geometry known as a θ {\displaystyle \theta } -summable spectral triple (also known as a θ {\displaystyle \theta
JLO_cocycle
Area of mathematics
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there
Discrete differential geometry
Discrete_differential_geometry
In mathematics, in the field of differential geometry, an Iwasawa manifold is a compact quotient of a 3-dimensional complex Heisenberg group by a cocompact
Iwasawa_manifold
Form of an object
other object properties, such as color, texture, or material type. In geometry, shape excludes information about the object's position, size, orientation
Shape
Geometric transformation
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale
Scaling_(geometry)
Spectral graph theory concept
In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal
Ramanujan_graph
Soviet and Russian mathematician (1938–2024)
Fomenko: Modern geometry- methods and applications, Vol.1-3, Springer, Graduate Texts in Mathematics (originally 1984, 1988, 1990, V.1 The geometry of surfaces
Sergei Novikov (mathematician)
Sergei_Novikov_(mathematician)
Mathematical function
Slepian functions are a class of spatio-spectrally concentrated functions that form an orthogonal basis for bandlimited or spacelimited spaces. That is
Slepian_function
Atiyah, M. F.; Patodi, V. K.; Singer, I. M. (1975). "Spectral asymmetry and Riemannian geometry I". Proceedings of the Cambridge Philosophical Society
Spectral_asymmetry
of interest. List of geometric shapes Spectral shape analysis Discrete Morse theory Discrete differential geometry Topological data analysis Equidimensional
Shape analysis (digital geometry)
Shape_analysis_(digital_geometry)
Mathematics award
Neves – "For outstanding contributions to several areas of differential geometry, including work on scalar curvature, geometric flows, and his solution
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Earth observation mission
Space in Friedrichshafen, Germany. The Sentinel-2 mission includes: Multi-spectral data with 13 bands in the visible, near infrared, and short wave infrared
Sentinel-2
Graduate-level textbooks in mathematics
Differential Forms in Analysis, Geometry and Physics Ilka Agricola, Thomas Friedrich 2002 978-0-8218-2951-6 53 Spectral Methods of Automorphic Forms Henryk
Graduate Studies in Mathematics
Graduate_Studies_in_Mathematics
Mathematical sequence
In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. It is usually seen nowadays
Leray_spectral_sequence
Transparent optical element with flat, polished surfaces that refract light
dispersive prism can be used to break white light up into its constituent spectral colors (the colors of the rainbow) to form a spectrum as described in the
Prism_(optics)
Planar movement within a Euclidean space without rotation
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction
Translation_(geometry)
Indian mathematician (1945–1976)
Raoul Bott. The joint work led to a series of papers, "Spectral Asymmetry and Riemannian Geometry" with Atiyah and Singer, in which the η-invariant was
Vijay_Kumar_Patodi
American mathematician (born 1977)
MR 2522659 Lurie, Jacob (2017), Higher Algebra Lurie, Jacob (2018), Spectral Algebraic Geometry "Jacob Lurie". Institute for Advanced Study. Retrieved August
Jacob_Lurie
Belgian mathematician
E7½ Hodge–de Rham spectral sequence Logarithmic form Kodaira vanishing theorem Moduli of algebraic curves Motive (algebraic geometry) Perverse sheaf Riemann–Hilbert
Pierre_Deligne
Thomas (2007), "Q-curvature, spectral invariants, and representation theory" (PDF), Symmetry, Integrability and Geometry: Methods and Applications, 3:
Polyakov_formula
recursion is a recursive definition of invariants of spectral curves. It has applications in enumerative geometry, random matrix theory, mathematical physics,
Topological_recursion
American mathematician (born 1974)
his Ph.D. from Harvard University in 1999, with a dissertation titled Spectral Curves, Opers And Integrable Systems supervised by Edward Frenkel. In 2012
David_Ben-Zvi
Brooks, 49, American mathematics professor, known for his work in spectral geometry and fractals. William Cooper, 92, English novelist. Cliff Gorman,
Deaths_in_September_2002
Measure used in functional analysis
particularly in functional analysis, a projection-valued measure, or spectral measure, is a function defined on certain subsets of a fixed set and whose
Projection-valued_measure
American mathematician
Technology in the field of symplectic geometry, and he has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics
Victor_Guillemin
matrix Positive-definite, positive-semidefinite matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal matrix, main
Outline_of_linear_algebra
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
Branch of mathematics
cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It is also a fundamental tool
K-theory
Indian computer scientist (born 1971)
algorithms, computational geometry, and computational learning theory, including the authorship of books on random projection and spectral methods. In 2008, he
Santosh_Vempala
Romanian Swedish mathematician
transforms, and the geometry of zeros of polynomials in one variable. Borcea and Petter Brändén collaborated on a project on the geometry of zeros of polynomials
Julius_Borcea
topology, a branch of mathematics, the Čech-to-derived functor spectral sequence is a spectral sequence that relates Čech cohomology of a sheaf and sheaf
Čech-to-derived functor spectral sequence
Čech-to-derived_functor_spectral_sequence
German mathematician (1862–1943)
commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical
David_Hilbert
American mathematician
Mathematics Institutions University of Massachusetts, Amherst Thesis Geometry of Operators and Spectral Analysis (1991) Doctoral advisor Ronald Coifman
Andrea_R._Nahmod
South African-born mathematician
Faculty, 2007–present, Institute for Advanced Study Sarnak, P. (1982). "Spectral Behavior of Quasi Periodic Potentials". Commun. Math. Phys. 84 (3): 377–401
Peter_Sarnak
American mathematician and Nobel Laureate (1928–2015)
made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists
John_Forbes_Nash_Jr.
Formulation of the finite element method
solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM)
Spectral_element_method
Type of program in computer graphics
Shaders act on data such as vertices and primitives, generate or morph geometries and fragments, and calculate the colors in a rendered image. Shaders can
Shader
SPECTRAL GEOMETRY
SPECTRAL GEOMETRY
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