Cohomological Automorphic Representations on Unitary Groups - Rahul Dalal
Joint IAS/PU Number Theory Seminar Topic: Applications of the Endoscopic Classification to Statistics of Cohomological Automorphic Representations on Unitary Groups Speaker: Rahul Dalal Affiliation: Johns Hopkins University Date: November 03, 2022 Consider the family of automorphic repre
From playlist Mathematics
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
Definition of a Group and Examples of Groups
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Group and Examples of Groups
From playlist Abstract Algebra
Bachir Bekka - On characters of infinite groups
Let G be a countable infinite group. Unless G is virtually abelian, a description of the unitary dual of G (that is, the equivalence classes of irreducible unitary representations of G) is hopeless, as a consequence of theorems of Glimm and Thoma. A sensible substitute for the unitary dual
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
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
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Abstract Algebra | Irreducibles and Primes in Integral Domains
We define the notion of an irreducible element and a prime element in the context of an arbitrary integral domain. Further, we give examples of irreducible elements that are not prime. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://
From playlist Abstract Algebra
Karol Życzkowski : Finite dimensional Hilbert space
Abstract: Among the set of all pure states living in a finite dimensional Hilbert space H_None distinguishes subsets of states satisfying some natural condition. One basis independent choice, consist in selecting the spin coherent states, corresponding to the SU(2) group, or generalized, S
From playlist Mathematical Physics
Complex, Hermitian, and Unitary Matrices
Remember when we talked about complex and imaginary numbers? All that a + bi stuff, it was a while ago. Well that can apply to matrices as well! We've been looking at real matrices thus far, but we can have imaginary or complex matrices if we have imaginary or complex terms as entries. Wha
From playlist Mathematics (All Of It)
Recovering quantum gates from few average fidelities - R. Kueng - Workshop 1 - CEB T2 2018
Richard Kueng (California Institute of Technology) / 17.05.2018 Recovering quantum gates from few average fidelities Characterizing quantum processes is a key task for the development of quantum technologies, especially at the noisy intermediate scale of today’s devices. One method for
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
[BOURBAKI 2018] 13/01/2018 - 2/4 - Raphaël BEUZART-PLESSIS
Progrès récents sur les conjectures de Gan-Gross-Prasad [d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.] Les conjectures de Gan-Gross-Prasad ont deux aspects: localement elles décrivent de façon explicite certaines lois de branchements entre représentations de groupes de Lie réels ou
From playlist BOURBAKI - 2018
Lucas Mason-Brown - Arthur's Conjectures and the Orbit Method for Real Reductive Groups
The most fundamental unsolved problem in the representation theory of Lie groups is the Problem of the Unitary Dual: given a reductive Lie group G, this problem asks for a parameterization of the set of irreducible unitary G-representations. There are two big "philosophies" for approaching
From playlist 2022 Summer School on the Langlands program
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q)
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q) In this lecture we back up and deploy the basis elements we eliminated in the su(2) and so(3) algebras when we enforced the determinants to be equal to 1. This expands the algebras to u(2) and o(3) and generates the groups U(2) a
From playlist Lie Groups and Lie Algebras
Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"
Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber
From playlist Actions of Tensor Categories on C*-algebras 2021
Gábor Szabó: "Classification of group actions on C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "Classification of group actions on C*-algebras" Gábor Szabó - KU Leuven Abstract: This talk will survey the classification of group actions on C*-algebras. One can often observe a rigid behavior of suitable classes of outer a
From playlist Actions of Tensor Categories on C*-algebras 2021
Stability, cohomology vanishing, and non-approximable groups - Andreas Thom
Stability and Testability Topic: Stability, cohomology vanishing, and non-approximable groups Speaker: Andreas Thom Affiliation: University of Dresden Date: December 2, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX In this lecture we count the degrees of freedom for the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Operator Scaling via Geodesically Convex Optimization, Invariant Theory... - Yuanzhi Li
Optimization, Complexity and Invariant Theory Topic: Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing Speaker: Yuanzhi Li Affiliation: Princeton University Date: June 7. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
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