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
Finding Peace in the Complex Plane
The visual representation of real versus imaginary numbers in the complex plane bothered me from the start. There is visually no difference but that is a problem since algebraically the two behave differently. The visual representation is not faithful to the algebraic representation. Consi
From playlist Summer of Math Exposition Youtube Videos
What are Real Numbers? | Don't Memorise
Watch this video to understand what Real Numbers are! To access all videos on Real Numbers, please enroll in our full course here - https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=3YwrcJxEbZw&utm_term=%7Bkeyword%7D In this video, w
From playlist Real Numbers
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
This video provides a basic introduction into real numbers. It explains how to distinguish them from imaginary numbers. It also discusses the difference between rational and irrational numbers as well as integers, natural numbers, and whole numbers. Examples include repeating and non-re
From playlist New Algebra Playlist
Identifying Sets of Real Numbers
This video provides several examples of identifying the sets a real number belongs to. Complete Video Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com
From playlist Number Sense - Properties of Real Numbers
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 ***
Imaginary Numbers, Functions of Complex Variables: 3D animations.
Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.
From playlist Physics
Jessica Fintzen - 1/2 Supercuspidal Representations: Construction, Classification, and Characters
We have seen in the first week of the summer school that the buildings blocks for irreducible representations of p-adic groups are the supercuspidal representations. In these talks we will explore explicit exhaustive constructions of these supercuspidal representations and their character
From playlist 2022 Summer School on the Langlands program
Representation theory: The Schur indicator
This is about the Schur indicator of a complex representation. It can be used to check whether an irreducible representation has in invariant bilinear form, and if so whether the form is symmetric or antisymmetric. As examples we check which representations of the dihedral group D8, the
From playlist Representation theory
Representations of p-adic reductive groups by Tasho Kaletha
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
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
Higgs bundles and higher Teichmüller components (Lecture 1) by Oscar Garcia
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
Representations of p-adic groups for non-experts - Jessica Fintzen
Short Talks by Postdoctoral Members Topic: Representations of p-adic groups for non-experts Speaker: Jessica Fintzen Affiliation: University of Cambridge and Duke University; Member, School of Mathematics Date: October 1, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Higgs bundles and higher Teichmüller components (Lecture 2) by Oscar García-Prada
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
Vigleik Angeltveit: The Picard group of Equivariant Stable Homotopy Theory
Vigleik Angeltveit: The Picard group of Equivariant Stable Homotopy Theory and the Slice Spectral Sequence 30 September 2021 Abstract: Equivariant stable homotopy groups are usually graded on the real representation ring. But it is possible to grade them on the Picard group instead. I wi
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Representations of p-adic groups - Jessica Fintzen
Workshop on Representation Theory and Geometry Topic: Representations of p-adic groups Speaker: Jessica Fintzen Affiliation: University of Cambridge and Duke University; Member, School of Mathematics Date: April 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)
From playlist Real Numbers
Higgs Bundles and Higher Teichmüller Spaces - Brian Collier
Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday Topic: Higgs Bundles and Higher Teichmüller spaces Speaker: Brian Collier Affiliation: University of California, Riverside Date: September 17, 2022 The Teichm\"uller space of a compact surface S is re
From playlist Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday