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
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
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 ***
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
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
Representation Theory as Gauge Theory - David Ben-Zvi [2016]
Slides for this talk: https://drive.google.com/file/d/1FHl_tIOjp26vuULi0gkSgoIN7PMnKLXK/view?usp=sharing Notes for this talk: https://drive.google.com/file/d/1BpP2Sz_zHWa_SQLM6DC6T8b4v_VKZs1A/view?usp=sharing David Ben-Zvi (University of Texas, Austin) Title: Representation Theory as G
From playlist Number 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
RT7.2. Finite Abelian Groups: Fourier Analysis
Representation Theory: With orthogonality of characters, we have an orthonormal basis of L^2(G). We note the basic philosophy behind the Fourier transform and apply it to the character basis. From this comes the definition of convolution, explored in 7.3. Course materials, including pro
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
Jens Eberhardt: Motivic Springer Theory
27 September 2021 Abstract: Algebras and their representations can often be constructed geometrically in terms of convolution of cycles. For example, the Springer correspondence describes how irreducible representations of a Weyl group can be realised in terms of a convolution action on
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Geordie Williamson, Challenges in modular representation theory
2019 Clay Research Conference plenary lecture
From playlist Geordie Williamson: Challenges in modular representation theory
Knot Categorification From Mirror Symmetry (Lecture- 1) by Mina Aganagic
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Nonlinear algebra, Lecture 9: "Representation Theory", by Mateusz Michalek
This is the ninth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Alex Fok, Equvariant twisted KK-theory of noncompact Lie groups
Global Noncommutative Geometry Seminar(Asia-Pacific), Oct. 25, 2021
From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)
A gentle introduction to group representation theory -Peter Buergisser
Optimization, Complexity and Invariant Theory Topic: A gentle introduction to group representation theory Speaker: Peter Buergisser Affiliation: Technical University of Berlin Date: June 4, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Katrin Wendland: How do quarter BPS states cease being BPS?
CONFERENCE Recorded during the meeting "Vertex Algebras and Representation Theory" the June 09, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovi
From playlist Mathematical Physics
Mumford-Tate Groups and Domains - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics March 28, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Modular forms of half-integral weight on exceptional groups
Joint IAS/Princeton University Number Theory Seminar Topic: Modular forms of half-integral weight on exceptional groups Speaker: Spencer Leslie Affiliation: Duke University Half-integral weight modular forms are classical objects with many important arithmetic applications. In terms of
From playlist Joint IAS/PU Number Theory Seminar
RT3. Equivalence and Examples (Expanded)
Representation Theory: We define equivalence of representations and give examples of irreducible representations for groups of low order. Then we use the commutator subgroup to characterize all one dimensional representations of G (characters) in terms of the abelianization of G. Course
From playlist Representation Theory
Zig-zag and the theta operator by Eknath Ghate
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019