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 ***
Representations of Finite Groups | Definitions and simple examples.
We define the notion of a representation of a group on a finite dimensional complex vector space. We also explore one and two dimensional representations of the cyclic group Zn. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.mich
From playlist Representations of Finite Groups
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
Representations of Finite Groups | A few more common examples.
We present a few more common examples of representations of finite groups. These include cyclic groups, dihedral groups, the quaternions, and the symmetric group. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net R
From playlist Representations of Finite Groups
Math 060 102317 Matrix Representations of Linear Transformations III
Review of the construction of the matrix representation of a linear transformation with respect to bases. Review: matrix representation of a linear transformation between Euclidean spaces with respect to bases (not necessarily the standard bases). Example.
From playlist Course 4: Linear Algebra (Fall 2017)
RT4.1.1: Complex Conjugate Representations
Representation Theory: We look at the complex conjugate of a representation in more detail. We present two equivalent formulations and show the conjugate is equivalent to the dual representation when pi is unitary.
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
Abstract Algebra | Normal Subgroups
We give the definition of a normal subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Supercuspidal L-packets - Tasho Kaletha
Computer Science/Discrete Mathematics Seminar I Topic: Supercuspidal L-packets Speaker: Tasho Kaletha Affiliation: Technion Date: March 5, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Regular supercuspidal representations - Tasho Kaletha
Beyond Endoscopy Topic: Regular supercuspidal representations Speaker: Tasho Kaletha, University of Toronto Date: Oct 01, 2016 Time/Room: 3:00pm-3:50pm/s-101 For more videos, visit http://video.ias.edu
From playlist Mathematics
Parahoric Subgroups and Supercuspidal Representations of p-Adic groups - Dick Gross
Dick Gross Harvard University December 9, 2010 This is a report on some joint work with Mark Reeder and Jiu-Kang Yu. I will review the theory of parahoric subgroups and consider the induced representation of a one-dimensional character of the pro-unipotent radical. A surprising fact is th
From playlist Mathematics
Local-global compatibility at primes dividing l - David Geraghty
David Geraghty Princeton University/Member, School of Mathematics March 23, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the im
From playlist Complex Numbers
Double covers of tori and the local Langlands correspondence - Tasho Kaletha
Workshop on Representation Theory and Geometry Topic: Double covers of tori and the local Langlands correspondence Speaker: Tasho Kaletha Affiliation: University of Michigan Date: April 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Transversality and super-rigidity in Gromov-Witten Theory (Lecture - 03) by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Vic Reiner, Lecture II - 11 February 2015
Vic Reiner (University of Minnesota) - Lecture II http://www.crm.sns.it/course/4036/ Many results in the combinatorics and invariant theory of reflection groups have q-analogues for the finite general linear groups GLn(Fq). These lectures will discuss several examples, and open questions
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
Arno Kret - Galois representations for the general symplectic group
In a recent preprint with Sug Woo Shin (https://arxiv.or/abs/1609.04223) I construct Galois representations corresponding for cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is
From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.
An explicit supercuspidal local Langlands correspondence - Tasho Kaletha
Joint IAS/Princeton University Number Theory Seminar Topic: An explicit supercuspidal local Langlands correspondence Speaker: Tasho Kaletha Affiliation: University of Michigan; von Neumann Fellow, School of Mathematics Date: October 29, 2020 For more video please visit http://video.ias.e
From playlist Mathematics
Talk by Charlotte Chan (MIT, USA)
Flag Varieties and Representations of p-adic Groups
From playlist Seminars: Representation Theory and Number Theory
RT4.1. Constructions from Linear Algebra (Expanded)
Representation Theory: We apply techniques from linear algebra to construct new representations from old ones. Constructions include direct sums, dual spaces, tensor products, and Hom spaces. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/U
From playlist Representation Theory