Computational group theory

Computational group theory

In mathematics, computational group theory is the study ofgroups by means of computers. It is concernedwith designing and analysing algorithms anddata structures to compute information about groups. The subjecthas attracted interest because for many interesting groups(including most of the sporadic groups) it is impracticalto perform calculations by hand. Important algorithms in computational group theory include: * the Schreier–Sims algorithm for finding the order of a permutation group * the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration * the for finding random elements of a group Two important computer algebra systems (CAS) used for group theory areGAP and Magma. Historically, other systems such as CAS (for character theory) and Cayley (a predecessor of Magma) were important. Some achievements of the field include: * complete enumeration of all finite groups of order less than 2000 * computation of representations for all the sporadic groups (Wikipedia).

Video thumbnail

p- groups - 1 by Heiko Dietrich

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

p- groups - 2 by Heiko Dietrich

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

Representation Theory(Repn Th) 5 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

Representation Theory(Repn Th) 4 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

p-groups - 4 by Heiko Dietrich

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

p-groups - 3 by Heiko Dietrich

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

Representation Theory(Repn Th) 3 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

Representation Theory(Repn Th) 1 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

p-groups - 5 by Heiko Dietrich

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

Teena Gerhardt - 1/3 Algebraic K-theory and Trace Methods

Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Video thumbnail

Lecture 2: Motivation

In this video, we give an important motivation for studying Topological Cyclic Homology, so called "trace methods". Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://w

From playlist Topological Cyclic Homology

Video thumbnail

Ximena Fernández 7/20/22: Morse theory for group presentations and the persistent fundamental group

Discrete Morse theory is a combinatorial tool to simplify the structure of a given (regular) CW-complex up to homotopy equivalence, in terms of the critical cells of discrete Morse functions. In this talk, I will present a refinement of this theory that guarantees not only a homotopy equiv

From playlist AATRN 2022

Video thumbnail

Xiang Tang: Cyclic Cocycles for Proper Lie Group Actions

Talk by Xiang Tang in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 23, 2021

From playlist Global Noncommutative Geometry Seminar (Europe)

Video thumbnail

Some Arithmetic Path Integrals - Minhyong Kim

Informal High Energy Theory Seminar Topic: Some Arithmetic Path Integrals Speaker: Minhyong Kim Affiliation: Oxford University Date: April 3, 2019 For more video please visit http://video.ias.edu

From playlist High Energy Theory

Video thumbnail

Christoph Winges: On the isomorphism conjecture for Waldhausen's algebraic K-theory of spaces

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I will survey recent progress on the isomorphism conjecture for Waldhausen's "algebraic K-theory of spaces" functor, and how this relates to the original isomorp

From playlist HIM Lectures: Junior Trimester Program "Topology"

Video thumbnail

Bettina EICK - Computational group theory, cohomology of groups and topological methods 2

The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

Video thumbnail

Oliver Röndigs: The first and second stable homotopy groups of motivic spheres over a field

The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"

From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"

Video thumbnail

What is Group Theory?

This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)

From playlist Summer of Math Exposition Youtube Videos

Related pages

Order (group theory) | List of small groups | Todd–Coxeter algorithm | Permutation group | Group representation | Schreier–Sims algorithm | Character theory | Mathematics | Coset enumeration | Charles Sims (mathematician) | Algorithm | Computer algebra system | Black box group | Group (mathematics)