Modular Forms | Modular Forms; Section 1 2
We define modular forms, and borrow an idea from representation theory to construct some examples. My Twitter: https://twitter.com/KristapsBalodi3 Fourier Theory (0:00) Definition of Modular Forms (8:02) In Search of Modularity (11:38) The Eisenstein Series (18:25)
From playlist Modular Forms
David Meyer (1/30/18): Some algebraic stability theorems for generalized persistence modules
From an algebraic point of view, generalized persistence modules can be interpreted as finitely-generated modules for a poset algebra. We prove an algebraic analogue of the isometry theorem of Bauer and Lesnick for a large class of posets. This theorem shows that for such posets, the int
From playlist AATRN 2018
Commutative algebra 44 Flat modules
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We summarize some of the properties of flat modules. In particular we show that for finitely presented modules over local ring
From playlist Commutative algebra
Partial fractions are SPECIAL! (Repeated linear factors)
► My Integrals course: https://www.kristakingmath.com/integrals-course The tricky thing about partial fractions is that there are four kinds of partial fractions problems. The kind of partial fractions decomposition you'll need to perform depends on the kinds of factors in your denominato
From playlist Integrals
Drinfeld Module Basics - part 01
This is a very elementary introduction to Drinfeld Modules. We just give the definitions. My wife helped me with this. Any mistakes I make are my fault.
From playlist Drinfeld Modules
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
2-Verma modules - Gregoire Naisse; Pedro Vaz
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: 2-Verma modules Speakers: Gregoire Naisse; Pedro Vaz Affiliation: University College London; University College London Date: November 18, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Weakly Modular Functions | The Geometry of SL2,Z, Section 1.4
We provide an alternative motivation for the definition of weakly modular functions. My Twitter: https://twitter.com/KristapsBalodi3 Weakly Modular Functions (0:00) Boring Functions on Compact Riemann Surfaces (2:06) Transforming the Transformation Property (9:15)
From playlist The Geometry of SL(2,Z)
Modular forms: Eisenstein series
This lecture is part of an online graduate course on modular forms. We give two ways of looking at modular forms: as functions of lattices in C, or as invariant forms. We use this to give two different ways of constructing Eisenstein series. For the other lectures in the course see http
From playlist Modular forms
Introduction to quantized enveloping algebras - Leonardo Maltoni
Quantum Groups Seminar Topic: Introduction to quantized enveloping algebras Speaker: Leonardo Maltoni Affiliation: Sorbonne University Date: January 28, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
The Drinfeld-Sokolov reduction of admissible representations of affine Lie algebras - Gurbir Dhillon
Workshop on Representation Theory and Geometry Topic: The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras Speaker: Gurbir Dhillon Affiliation: Yale University Date: April 03, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of G-bundles
Verlinde Dimension Formula Topic: Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of G-bundles Speaker: Shrawan Kumar Affiliation: University of North Carolina; Member, School of Mathematics
From playlist Verlinde Dimension Formula
Gabriele Rembado - Moduli Spaces of Irregular Singular Connections: Quantization and Braiding
Holomorphic connections on Riemann surfaces have been widely studied, as well as their monodromy representations. Their moduli spaces have natural Poisson/symplectic structures, and they can be both deformed and quantized: varying the Riemann surface structure leads to the action of mappin
From playlist Workshop on Quantum Geometry
Ben Elias: Categorifying Hecke algebras at prime roots of unity
Thirty years ago, Soergel changed the paradigm with his algebraic construction of the Hecke category. This is a categorification of the Hecke algebra at a generic parameter, where the parameter is categorified by a grading shift. One key open problem in categorification is to categorify He
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Representation theory and geometry – Geordie Williamson – ICM2018
Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor
From playlist Plenary Lectures
Counting and Constraining Gravitational Scattering matrices (Lecture 2) by Shiraz Minwalla
RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lectures
From playlist Recent Developments in S-matrix Theory (Online)
Quantum groups at roots of unity - Jay Taylor
Quantum Groups Seminar Topic: Quantum groups at roots of unity Speaker: Jay Taylor Affiliation: University of Southern California; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Learn how to divide rational expressions. A rational expression is an expression in the form of a fraction, usually having variable(s) in the denominator. Recall that to divide by a fraction, we multiply by the reciprocal of the fraction. The same rule applies when we want to divide by a r
From playlist How to Divide Rational Expressions #Rational