In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras (up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized family of Lie algebras. (Sometimes two of the groups are included in the infinite families, giving 9 instead of 11 classes.) The classification is important in geometry and physics, because the associated Lie groups serve as symmetry groups of 3-dimensional Riemannian manifolds. It is named for Luigi Bianchi, who worked it out in 1898. The term "Bianchi classification" is also used for similar classifications in other dimensions and for classifications of complex Lie algebras. (Wikipedia).
Lie groups: Bianchi classification
This lecture is part of an online graduate course on Lie groups. We give a sketch of the Bianchi classification of the Lie algebras and groups of dimension at most 3. We mention that this is related to the Thurston geometries of 3-manifolds. For the other lectures in the course see ht
From playlist Lie groups
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Robert BRYANT - Algebraically Constrained Special Holonomy Metrics...
Robert BRYANT - Algebraically Constrained Special Holonomy Metrics and Second-order Associative 3-folds There are various methods known now for constructing more-or-less explicit metrics with special holonomy; most of these rely on assumptions of symmetry and/or reduction. Another promisi
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups
24th Workshop in Geometric Topology, Calvin College, June 29, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Growth of Bianchi modular forms - Weibo Fu
Arithmetic Groups Topic: Growth of Bianchi modular forms Speaker: Weibo Fu Affiliation: Princeton University Date: March 30, 2022 In this talk, I will establish a sharp bound on the growth of cuspidal Bianchi modular forms. By the Eichler-Shimura isomorphism, we actually give a sharp bou
From playlist Mathematics
Tetrahedral hyperbolic 3-manifolds and links by Andrei Vesnin
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Haluk SENGUN - Cohomology of arithmetic groups and number theory: geometric, ... 2
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Peter Scholze - Locally symmetric spaces, and Galois representations (4)
Lecture: Locally symmetric spaces, and Galois representations Speaker: Peter Scholze (The University of Bonn, Germany) Date: 25 Mar 2014, 11:30 AM Venue: AG 66, TIFR, Mumbai One of the most studied objects in mathematics is the modular curve, given as the locally symmetric space whic
From playlist Locally symmetric spaces, and Galois representations
Exceptional holonomy and related geometric structures: Basic theory - Simon Donaldson
Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Basic theory. Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 3, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics