Andrew Putman - The Steinberg representation is irreducible
The Steinberg representation is a topologically-defined representation of groups like GL_n(k) that plays a fundamental role in the cohomology of arithmetic groups. The main theorem I will discuss says that for infinite fields k, the Steinberg representation is irreducible. For finite field
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Kronecker delta and Levi-Civita symbol | Lecture 7 | Vector Calculus for Engineers
Definition of the Kronecker delta and the Levi-Civita symbol (sometimes called the permutation symbol or Levi-Civita tensor). The relationship between the Kronecker delta and the Levi-Civita symbol is discussed. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engin
From playlist Vector Calculus for Engineers
Theory of numbers: Jacobi symbol
This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t
From playlist Theory of numbers
Nuclide Symbols: Atomic Number, Mass Number, Ions, and Isotopes
How do we represent an atom, with all of its protons, neutrons, and electrons? With nuclide symbols, of course! These show the type of element, as well as the atomic number, mass number, and electrical charge of an atom. That's all you need to know! Watch the whole General Chemistry playl
From playlist General Chemistry
The 2009 Nobel Prize in Physics - Sixty Symbols
As the Nobel Prize in Physics is awarded, we look at who won and how it's decided. More physics at http://www.sixtysymbols.com/ More Nobel videos: http://bit.ly/SSNobel
From playlist Nobel Prize Videos - Sixty Symbols
Neutrinos and the 2015 Nobel Prize in Physics - Sixty Symbols
The 2015 Nobel Prize in Physics goes to Takaaki Kajita and Arthur B. McDonald for showing that Neutrinos have mass. More Nobel winners: http://bit.ly/SSNobel This video features Ed Copeland, Michael Merrifield and Meghan Gray. More Neutrino videos: https://www.youtube.com/playlist?list=
From playlist Nobel Prize Videos - Sixty Symbols
Harold Steinacker - Covariant Cosmological Quantum Space-Time
Covariant Cosmological Quantum Space-Time: Higher-spin and Gravity in the IKKT Matrix Model https://indico.math.cnrs.fr/event/4272/attachments/2260/2717/IHESConference_Harold_STEINACKER.pdf
From playlist Space Time Matrices
Identify the Symbols in Statistics
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Identify the Symbols in Statistics
From playlist Statistics
Zachary Himes - On not the rational dualizing module for $\text{Aut}(F_n)$
Bestvina--Feighn proved that $\text{Aut}(F_n)$ is a rational duality group, i.e. there is a $\mathbb{Q}[\text{Aut}(F_n)]$-module, called the rational dualizing module, and a form of Poincar\'e duality relating the rational cohomology of $\text{Aut}(F_n)$ to its homology with coefficients i
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Eisenstein Ideals: A Link Between Geometry and Arithmetic - Emmanuel Lecouturier
Short Talks by Postdoctoral Members Topic: Eisenstein Ideals: A Link Between Geometry and Arithmetic Speaker: Emmanuel Lecouturier Affiliation: Member, School of Mathematics Date: September 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
This video introduces the identity matrix and illustrates the properties of the identity matrix. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
Modular symbols and arithmetic - Romyar Sharifi
Locally Symmetric Spaces Seminar Topic: Modular symbols and arithmetic Speaker: Romyar Sharifi Affiliation: University of California; Member, School of Mathematics Date: January 16, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
The K-ring of Steinberg varieties - Pablo Boixeda Alvarez
Geometric and Modular Representation Theory Seminar Topic: The K-ring of Steinberg varieties Speaker: Pablo Boixeda Alvarez Affiliation: Member, School of Mathematics Date: February 03, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Jennifer WILSON - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 1
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Jonny Steinberg - Talks About Nelson and Winnie Mandela’s Marriage
Jonny Steinberg is a South African writer and scholar from the University of Oxford. He is at Yale as a visiting scholar in the Council on African Studies at the MacMillan Center. Professor Steinberg is the author of several books that explore South African people and institutions in the w
From playlist The MacMillan Report
Modular symbols and arithmetic II - Romyar Sharifi
Locally Symmetric Spaces Seminar Topic: Modular symbols and arithmetic II Speaker: Romyar Sharifi Affiliation: University of California; Member, School of Mathematics Date: January 30, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Mark W. McConnell: Computing Hecke operators for cohomology of arithmetic subgroups of SL_n(Z)
Abstract: We will describe two projects. The first which is joint with Avner Ash and Paul Gunnells, concerns arithmetic subgroups Γ of G=SL_4(Z). We compute the cohomology of Γ∖G/K, focusing on the cuspidal degree H^5. We compute a range of Hecke operators on this cohomology. We fi Galois
From playlist Number Theory
On Sharifi’s Conjectures and Generalizations by Emmanuel Lecouturier
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 10
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Introduction to number theory lecture 36 Kronecker symbol
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We define the Kronecker symbol and summarize its properties. The textbook is "An introduc
From playlist Introduction to number theory (Berkeley Math 115)