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In algebra, Solomon's descent algebra of a Coxeter group is a subalgebra of the integral group ring of the Coxeter group, introduced by Solomon (1976)
Descent_algebra
In algebra, the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations or MPR Hopf algebra is a Hopf algebra with a basis of all elements of all the
Hopf_algebra_of_permutations
Mathematical concept that extends the intuitive idea of gluing in topology
theorems of descent and techniques of existence (see FGA) connecting the descent question with the representable functor question in algebraic geometry in
Descent_(mathematics)
Mathematical concept
descent algebra. The direct sum of the peak algebras for all n has a natural structure of a Hopf algebra. Nyman, Kathryn L. (2003), "The peak algebra
Peak_algebra
Generalization of algebraic spaces or schemes
if their underlying schemes or algebraic spaces are smooth. After Grothendieck developed the general theory of descent, and Giraud the general theory
Algebraic_stack
Web of human social relationships
number of related concepts and terms in the study of kinship, such as descent, descent group, lineage, affinity/affine, consanguinity/cognate and fictive
Kinship
Islamic mathematician (c. 780 – c. 850)
details are known about al-Khwarizmi's life. His popularizing treatise on algebra, compiled between 813 and 833 as Al-Jabr (The Compendious Book on Calculation
Al-Khwarizmi
Beck–Chevalley condition for p, the category of descent data is canonically equivalent to the category of algebras of the monad induced by p ! , p ∗ {\displaystyle
Monadic_descent
Generalisation of a sheaf; a fibered category that admits effective descent
(2005), "Grothendieck topologies, fibered categories and descent theory", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence, R
Stack_(mathematics)
Study of categorified structures
parametrized categories), topoi, effective descent, and enriched and internal categories. In higher-dimensional algebra (HDA), a double groupoid is a generalisation
Higher-dimensional_algebra
Operation in algebra and mathematics
in different fields such as topos theory and topics in algebraic geometry related to descent. A first example of a comonadic adjunction is the adjunction
Monad_(category_theory)
Derived descent
In algebraic geometry, a cohomological descent is, roughly, a "derived" version of a fully faithful descent in the classical descent theory. This point
Cohomological_descent
Branch of mathematics
as descent theory. This works to some extent: for instance, Dixmier's enveloping algebras may be thought of as working out non-commutative algebraic geometry
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Theorem in category theory
relation with the descent theory, which plays a role in sheaf and stack theory, as well as in the Alexander Grothendieck's approach to algebraic geometry. Most
Beck's_monadicity_theorem
American actress, mathematics writer, and education advocate (born 1975)
non-fiction books about mathematics: Math Doesn't Suck, Kiss My Math, Hot X: Algebra Exposed, Girls Get Curves: Geometry Takes Shape, Goodnight, Numbers, and
Danica_McKellar
Restriction of scalars
restriction") is a functor which, for any finite extension of fields L/k and any algebraic variety X over L, produces another variety ResL/kX, defined over k. It
Weil_restriction
Generalization of a scheme
In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory
Algebraic_space
Technique from algebraic geometry
Faithfully flat descent or flat descent is a technique from algebraic geometry, allowing one to draw conclusions about objects on the target of a faithfully
Faithfully_flat_descent
In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn
Quasisymmetric_function
Branch of mathematics
Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts
Derived_algebraic_geometry
French mathematician (1928–2014)
of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory
Alexander_Grothendieck
Severi–Brauer variety over a field K is an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated
Severi–Brauer_variety
American mathematician (1916–2001)
Information Age. Shannon was among the first to describe the use of Boolean algebra—essential to all digital electronic circuits—and helped found the field
Claude_Shannon
Mathematical proof technique using contradiction
not having algebra, worked out a geometric proof by infinite descent (John Horton Conway presented another geometric proof by infinite descent that may
Proof_by_infinite_descent
Austrian mathematician (1898–1962)
mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory
Emil_Artin
Canadian mathematician
Edmund F. Robertson and Michael D. Atkinson, with a thesis titled The Descent Algebras of Coxeter Groups. Van Willigenburg was awarded the Krieger–Nelson
Stephanie_van_Willigenburg
German mathematician (born 1974)
(born in 1974) is a German mathematician. He specializes in arithmetic algebraic geometry (étale fundamental group, anabelian geometry and other topics)
Jakob_Stix
Counterexample in algebraic geometry
In algebraic geometry, Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds found by Heisuke Hironaka (1960,
Hironaka's_example
Topos Derived category Descent (category theory) Grothendieck's Galois theory Algebraic stack Gerbe Étale cohomology Motive (algebraic geometry) Motivic cohomology
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Construction in algebraic geometry
In mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special
Fiber_product_of_schemes
American mathematician (born 1937)
(born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won
David_Mumford
American mathematician (born 1934)
of Technology Mathematics Department, known for his contributions to algebraic geometry. Artin was born in Hamburg, Germany, and brought up in Indiana
Michael_Artin
Israeli mathematician (1921–1994)
polynomial identities (PI-rings), division algebras, the general theory of radicals, and the Amitsur complex in descent theory. His collected works, published
Shimshon_Amitsur
Conjectures connecting number theory and geometry
structure of Galois groups in algebraic number theory to automorphic forms and, more generally, the representation theory of algebraic groups over local fields
Langlands_program
Mathematics book
(2005), "Grothendieck topologies, fibered categories and descent theory", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence, R
Fondements de la Géometrie Algébrique
Fondements_de_la_Géometrie_Algébrique
Simpson, Algebraic (geometric) n-stacks, 1996, arXiv:alg-geom/9609014. André Hirschowitz, Carlos Simpson, Descente pour les n-champs (Descent for n-stacks)
Higher_stack
Algebraic geometry
"Notes on Grothendieck topologies, fibered categories and descent theory" (PDF). Algebraic Geometry I: Schemes. Springer Studium Mathematik - Master.
Descent_along_torsors
Fermat's theorem on sums of two squares Fermat theory Pell–Fermat equation 12007 Fermat Fermat (computer algebra system) Fermat (crater) Fermat Prize
List of things named after Pierre de Fermat
List_of_things_named_after_Pierre_de_Fermat
Algebraic geometry analog of a principal bundle in algebraic topology
In algebraic geometry, a torsor or a principal bundle is an analogue of a principal bundle in algebraic topology. Because there are few open sets in Zariski
Torsor_(algebraic_geometry)
Transforms equations for numerical solution
preconditioned problem is then usually solved by an iterative method. In linear algebra and numerical analysis, a preconditioner P {\displaystyle P} of a matrix
Preconditioner
Inequality from distance to a zero of a real analytic function
In real algebraic geometry, the Łojasiewicz inequality, named after Stanisław Łojasiewicz, gives an upper bound for the distance of a point to the nearest
Łojasiewicz_inequality
Canadian mathematician (born 1988)
mathematician at the University of Toronto specialising in Arithmetic geometry , Algebraic geometry and related areas. He was awarded the SASTRA Ramanujan Prize
Jacob_Tsimerman
Ethnic group native to the island of Ireland
Huguenot descent, was the creator of the Beaufort scale for indicating wind force. George Boole (1815–1864), the mathematician who invented Boolean algebra, spent
Irish_people
American poet (1959–2007)
and songwriter, best known for her work with the new wave musical group Algebra Suicide, along with her husband Don Hedeker. Lydia Tomkiw was born in Chicago's
Lydia_Tomkiw
3D imaging technology
for 3D ECT include Newton-Raphson, Landweber iteration and steepest descent algebraic reconstruction and simultaneous reconstruction techniques, and model-based
Three-dimensional electrical capacitance tomography
Three-dimensional_electrical_capacitance_tomography
British-American scientist (born 1959)
British-American computer scientist, physicist, and businessman. He works in computer algebra and theoretical physics. In 2012, he was named a fellow of the American
Stephen_Wolfram
American mathematician (born 1974)
Kiran Sridhara Kedlaya (/ˈkɪrən ˈʃriːdər kɛdˈlɑːjə/ KIRR-ən SHREE-dər ked-LAH-yə; born July 1974) is an American mathematician. He currently is a professor
Kiran_Kedlaya
Mathematical heuristic
Grothendieck, who made extensive use of it in treating foundational aspects of algebraic geometry. Outside that field, it has been influential particularly on
Grothendieck's relative point of view
Grothendieck's_relative_point_of_view
Mathematical optimization method
Attouch, H.; Bolte, J.; Svaiter, B. F. (2011). "Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting
Backtracking_line_search
Direct summand of a free module (mathematics)
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over
Projective_module
Construction of a ring of fractions
In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces
Localization (commutative algebra)
Localization_(commutative_algebra)
Iterative method used to solve a linear system of equations
semi-definite matrix, so it has no negative eigenvalues. A step of gradient descent is x ( k + 1 ) = x ( k ) − t ∇ F ( x ( k ) ) = x ( k ) − t ( A x ( k )
Modified_Richardson_iteration
American mathematician (born 1983)
in 2022. He has been noted for the linkages that he has found between algebraic geometry and combinatorics. Huh was born in Stanford, California while
June_Huh
ethnicities. This list also includes people of German Jewish descent. Americans of German descent live in nearly every American county, from the East Coast
List_of_German_Americans
Canadian-American mathematician
(born February 22, 1970) is a Canadian-American mathematician working in algebraic geometry. He is the current president of the American Mathematical Society
Ravi_Vakil
Russian-American mathematician
is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at
Edward_Frenkel
theory of fibrations, toposes, indexed categories, descent theory, categorical logic, and algebraic geometry. It is named after Jonathan Mock Beck and
Beck–Chevalley_condition
Operation in algebra
In algebra, a change of rings is an operation of changing a coefficient ring to another. Given a ring homomorphism f : R → S {\displaystyle f:R\to S}
Change_of_rings
American game show winner and child prodigy (born 1984)
where he took Algebra and French accompanied by his mother, and Nova Independent High School, an alternative high school. His Algebra teacher questioned
Michael_Kearney
1960–67 foundational treatise on algebraic geometry by Alexander Grothendieck
French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published
Éléments de géométrie algébrique
Éléments_de_géométrie_algébrique
English mathematician and philosopher (1815–1864)
differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854), which contains Boolean algebra. Boolean logic, essential
George_Boole
Application of homotopy to algebraic varieties
In algebraic geometry and algebraic topology, branches of mathematics, A1 homotopy theory or motivic homotopy theory is a way to apply the techniques of
A¹_homotopy_theory
of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Type of feedforward neural network
that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output
Multilayer_perceptron
In algebraic geometry and synthetic differential geometry, a Grothendieck connection is a way of viewing connections in terms of descent data from infinitesimal
Grothendieck_connection
mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Algorithmic runtime requirements for common math procedures
1137/0209036. von zur Gathen, J.; Gerhard, J. (2013). Modern Computer Algebra (3rd ed.). Cambridge University Press. ISBN 9781139856065. Borwein, J.;
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
History of maths
Categories of abstract algebraic structures including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Irish mathematician and physicist (1805–1865)
mathematician, physicist, and astronomer who made numerous major contributions to algebra, classical mechanics, and optics. His theoretical works and mathematical
William_Rowan_Hamilton
Theoretical object in mathematics
by Vezzani. Nikolai Durov constructed F1 as a commutative algebraic monad. Borger used descent to construct it from the finite fields and the integers.
Field_with_one_element
Group of symmetries of an n-dimensional hypercube
the symplectic groups and the orthogonal groups and their associated Lie algebras, and in combinatorics, where they may be viewed as a signed version of
Hyperoctahedral_group
American mathematician
Wei Ho is an American mathematician specializing in number theory, algebraic geometry, arithmetic geometry, and representation theory. She is an associate
Wei_Ho
topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also plays a fundamental role in the theory of descent (faithfully
Flat_topology
Generalization of algebraic variety
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of an algebraic variety in several ways, such as taking
Scheme_(mathematics)
Open conjecture that no real circulant Hadamard matrix has order greater than 4
1090/S0002-9947-03-03365-8. Lander, Eric S. (1983). Symmetric Designs: An Algebraic Approach. London Mathematical Society Lecture Note Series. Vol. 74. Cambridge
Ryser's conjecture on circulant Hadamard matrices
Ryser's_conjecture_on_circulant_Hadamard_matrices
American-Turkish mathematician (born 1992)
tenth problem has a negative answer over the ring of integers of every algebraic number field. On July 19, 2026, Alpöge presented an explicit counterexample
Levent_Alpöge
MR 0354655. Kerz, Moritz; Strunk, Florian; Tamme, Georg (2018). "Algebraic K-theory and descent for blow-ups". Inventiones Mathematicae. 211 (2): 523–577. arXiv:1611
Perfect_complex
(probability) Iterative method (numerical analysis) Jacobi method (linear algebra) Largest remainder method (voting systems) Level-set method Linear combination
List of mathematics-based methods
List_of_mathematics-based_methods
Mathematical optimization algorithm
algorithm after cancelling α k {\displaystyle \alpha _{k}} . using LinearAlgebra """ x = conjugate_gradient(A, b, x0 = zero(b); atol=length(b)*eps(norm(b))
Conjugate_gradient_method
University of Kansas. She specializes in set theory, topology, Boolean algebras, and mathematics education. James J. Hughes (born May 27, 1961) is an American
List_of_American_Buddhists
American mathematician (born 1942)
professor of mathematics at the University of Illinois Urbana-Champaign. An algebraic geometer, Haboush is the namesake of Haboush's theorem, which he proved
William_Haboush
Ordering obtained by a single shuffle
tricks. Riffle shuffles may be used to define the shuffle algebra. This is a Hopf algebra where the basis is a set of words, and the product is the shuffle
Riffle_shuffle_permutation
Russian-American mathematician
works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded the
Alexander_Beilinson
Chinese mathematician (born 1991)
transfer exam, she switched her academic major to mathematics, focusing on algebraic analysis and mathematical analysis. Wang graduated from Peking University
Hong_Wang
Israeli mathematician (born 1982)
Schlank, Tomer; Yanovski, Lior (2024). "Descent and cyclotomic redshift for chromatically localized algebraic 𝐾-theory". Journal of the American Mathematical
Tomer_Schlank
Branch of mathematics
structures that are often specified via algebraic operations and defining identities are Heyting algebras and Boolean algebras, which both introduce a new operation
Order_theory
French mathematician (1789–1857)
field of complex analysis, and the study of permutation groups in abstract algebra. Cauchy also contributed to a number of topics in mathematical physics
Augustin-Louis_Cauchy
Type of infinite structure
(S_{n})_{n=0}^{\infty }} such that S n {\displaystyle S_{n}} is a boolean algebra of subsets of M n {\displaystyle M^{n}} if D ∈ S n {\displaystyle D\in
O-minimal_theory
Concept in category theory
to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull-backs)
Fibred_category
Canadian actor (born 1989)
'homework' that included reading biographies of scientists and studying algebra". Upon his arrival in Kingston, Liu attended Sydenham Public School. He
Simu_Liu
Japanese-born American mathematician (1928–2026)
Japanese-born American mathematician, specializing in number theory and algebraic groups. Ono was born in Nishinomiya, Japan, on 18 December 1928. He received
Takashi_Ono_(mathematician)
part Japanese descent Sally Amaki, singer and voice actress, member of idol group 22/7 Ella Anderson, actress; is of 1/8th Japanese descent on her father's
List_of_Japanese_Americans
Romanian prose writer, poet, and political (1879–1951)
and understood their meaning much later in life. His first contact with algebra was through a book that he reviewed in an antiquarian's shop. He then applied
I._C._Vissarion
American football coach (born 1974)
he majored in history, Bajakian taught a variety of math classes, from algebra and geometry to trigonometry and pre-calculus, at the Delbarton School
Mike_Bajakian
Award ceremony for television programming of 2023 and 2024
Program Percy Jackson and the Olympians: "I Accidentally Vaporize My Pre-Algebra Teacher" – Rick Riordan, Jonathan E. Steinberg (Disney+) High School Musical:
3rd Children's and Family Emmy Awards
3rd_Children's_and_Family_Emmy_Awards
focused on Welsh topics in the 1860s. A few schools taught subjects such as algebra, chemistry, astronomy and training for employment. An 1864 manual on teaching
History of education in Wales (1701–1870)
History_of_education_in_Wales_(1701–1870)
Scheme theory concept
In mathematics, in particular in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every
Flat_morphism
American mathematician
an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian
Lauren Williams (mathematician)
Lauren_Williams_(mathematician)
Representation theory
space, this *-algebra is commutative. The closure of its (the Hecke algebra's) image in the operator norm is a non-unital commutative C* algebra A {\displaystyle
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Australian mathematician (born 1981)
representation theory, locally symmetric spaces, ergodic theory, and algebraic topology. He was the first Australian to have won medals at both the International
Akshay_Venkatesh
DESCENT ALGEBRA
DESCENT ALGEBRA
Girl/Female
Biblical
Strange descent.
Boy/Male
American, Australian, British, English
Surname Referring to Derwent River in England
Boy/Male
American, Australian, French, Greek, Hebrew, Scandinavian
Descend
Boy/Male
Indian, Sanskrit
Of Noble Descent
Boy/Male
Indian, Tamil
World
Boy/Male
Hindu
Of sacred descent
Surname or Lastname
English
English : from Middle English besant, the name of a gold coin (via Old French from Latin (nummus) byzantius, so called because it was first minted at Byzantium). The surname arose as a metonymic occupational name for a minter or moneyer or else as a nickname for a man who was considered to be rich or miserly.
Biblical
one that commands; he that descends,one that descending,descent
Boy/Male
Hindu
Of noble descent
Boy/Male
Tamil
Of sacred descent
Boy/Male
Australian, Hebrew, Italian
Descend
Boy/Male
Hindu
A noble descent
Girl/Female
Irish
Bard.
Boy/Male
Tamil
A noble descent
Boy/Male
American, Australian, British, English, Hebrew
Rules by the Spear; He Descends; Descent
Girl/Female
French
To create.
Boy/Male
Australian, Dutch, Hebrew
Descend
Biblical
strange descent
Boy/Male
African, American, British, Christian, Dutch, English, Hawaiian, Hebrew, Hindu, Indian, Jamaican
Descends; Descending One who Rules; Descent
Boy/Male
Tamil
Of noble descent
DESCENT ALGEBRA
DESCENT ALGEBRA
DESCENT ALGEBRA
DESCENT ALGEBRA
DESCENT ALGEBRA
DESCENT ALGEBRA
DESCENT ALGEBRA