Representation theory: Introduction
This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr
From playlist Representation theory
RT6. Representations on Function Spaces
Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in
From playlist Representation Theory
RT1: Representation Theory Basics
Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe
From playlist *** The Good Stuff ***
RT7.3. Finite Abelian Groups: Convolution
Representation Theory: We define convolution of two functions on L^2(G) and note general properties. Three themes: convolution as an analogue of matrix multiplication, convolution with character as an orthogonal projection on L^2(G), and using using convolution to project onto irreduci
From playlist Representation Theory
Representation theory: Orthogonality relations
This lecture is about the orthogonality relations of the character table of complex representations of a finite group. We show that these representations are unitary and deduce that they are all sums of irreducible representations. We then prove Schur's lemma describing the dimension of t
From playlist Representation theory
RT8.2. Finite Groups: Classification of Irreducibles
Representation Theory: Using the Schur orthogonality relations, we obtain an orthonormal basis of L^2(G) using matrix coefficients of irreducible representations. This shows the sum of squares of dimensions of irreducibles equals |G|. We also obtain an orthonormal basis of Class(G) usin
From playlist Representation Theory
Representation theory: Abelian groups
This lecture discusses the complex representations of finite abelian groups. We show that any group is iomorphic to its dual (the group of 1-dimensional representations, and isomorphic to its double dual in a canonical way (Pontryagin duality). We check the orthogonality relations for the
From playlist Representation theory
Representation theory: Induced representations
We define induced representations of finite groups in two ways as either left or right adjoints of the restriction functor. We calculate the character of an induced representation, and give an example of an induced representation of S3.
From playlist Representation theory
Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups - Sam Nariman
Workshop on the h-principle and beyond Topic: Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups Speaker: Sam Nariman Affiliation: Purdue University Date: November 1, 2021 Abstract: I will discuss a remarkable generalization of Mather’s theorem by Thurston
From playlist Mathematics
Hyperbolic surfaces and their Teichmüller spaces (Lecture - 02) by Subhojoy Gupta
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Exceptional holonomy and related geometric structures: Examples and moduli theory - Simon Donaldson
Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Examples and moduli theory. Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 4, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Thin groups as monodromy groups, Part I - Jordan Ellenberg (University of Wisconsin-Madison)
Thin groups as monodromy groups Jordan Ellenberg University of Wisconsin – Madison We discuss various algebro-geometric contexts in which thin groups appear as monodromy groups attached to families of varieties over curves. http://www.msri.org/workshops/652/schedules/14578
From playlist Number Theory
Matthew D. Foreman: A symbolic representation of Anosov-Katok diffeomorphisms
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Logic and Foundations
Representation Theory: We explain unitarity and invariant inner products for representations of finite groups. Full reducibility of such representations is derived. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/UR-RepTheory.html
From playlist Representation Theory
Joel Hass - Lecture 5 - Algorithms and complexity in the theory of knots and manifolds - 22/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Benson Farb, Part 2: Surface bundles, mapping class groups, moduli spaces, and cohomology
29th Workshop in Geometric Topology, Oregon State University, June 29, 2012
From playlist Benson Farb: 29th Workshop in Geometric Topology
A New Poisson Bracket Identity for Gravity by Madhavan Varadarajan
Bangalore Area String Meeting URL: http://www.icts.res.in/discussion_meeting/BASM2016/ DATES: Monday 25 Jul, 2016 - Wednesday 27 Jul, 2016 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore DESCRIPTION: This meeting is designed to bring together string theorists working in the Bangalore
From playlist Bangalore Area String Meeting
Contact invariants in sutured monopole and instanton homology - Steven Sivek
Steven Sivek University of Warwick March 5, 2014 Kronheimer and Mrowka recently used monopole Floer homology to define an invariant of sutured manifolds, following work of Juhász in Heegaard Floer homology. In this talk, I will construct an invariant of a contact structure on a 3-manifold
From playlist Mathematics
Representation theory: Frobenius groups
We recall the definition of a Frobenius group as a transitive permutation group such that any element fixing two points is the identity. Then we prove Frobenius's theorem that the identity together with the elements fixing no points is a normal subgroup. The proof uses induced representati
From playlist Representation theory
P=WP=W: a strange identity for GL(2,ℂ)GL(2,C) - Mark deCataldo
Mark deCataldo Stony Brook University; Member, School of Mathematics November 24, 2014 Start with a compact Riemann surface XX and a complex reductive group GG, like GL(n,ℂ)GL(n,C). According to Hitchin-Simpson's ``non abelian Hodge theory", the pair (X,G)(X,G) comes with two new complex
From playlist Mathematics