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)
This lecture is part of an online graduate course on modular forms. We first show that the number of zeros of a (level 1 holomorphic) modular form in a fundamental domain is weight/12, and use this to show that the graded ring of modular forms is the ring of polynomials in E4 and E6. Fo
From playlist Modular forms
Modular Functions | Modular Forms; Section 1.1
In this video we introduce the notion of modular functions. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Weakly Modular Functions (2:10) Factor of Automorphy (8:58) Checking the Generators (15:04) The Nome Map (16:35) Modular Functions (22:10)
From playlist Modular Forms
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
Modular forms: Modular functions
This lecture is part of an online graduate course on modular forms. We classify all meromorphic modular functions, showing that they are all rational functions of the elliptic modular function j. As an application of j we use it to prove Picard's theorem that a non-constant meromorphic
From playlist Modular forms
Francis Brown: Modular graph functions and non holomorphic modular forms
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: Modular graph functions are non-holomorphic modular forms arising from string perturbation theory in genus 1 studied by Green, Russo, Vanhove,
From playlist Workshop: "Amplitudes and Periods"
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
Claudia Alfes: Traces of CM values and geodesic cycle integrals of modular functions
In this talk we give an introduction to the study of generating series of the traces of CM values and geodesic cycle integrals of different modular functions. First we define modular forms and harmonic Maass forms. Then we briefly discuss the theory of theta lifts that gives a conceptual f
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
N=2* SU(2) Supersymmetric Yang-Mills Theory and Four-Manifold Invariants - Gregory Moore
High Energy Theory Seminar N=2* SU(2) Supersymmetric Yang-Mills Theory and Four-Manifold Invariants Speaker: Gregory Moore Affiliation: Rutgers University Date: March 15, 2021 For more video please visit http://video.ias.edu
From playlist IAS High Energy Theory Seminar
Francis Brown - 2/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
Modular forms: Discriminant and E2
This lecture is part of an online graduate course on modular forms. We discuss the infinite product of the discriminant function and relate it to the fact that the Eisenstein series E2 is not quite a modular form. We then sketch Siegel's proof of the infinite product for the discriminant
From playlist Modular forms
Two Dimensional Galois Representations Over Imaginary Quadratic Fields - Andrei Jorza
Two Dimensional Galois Representations Over Imaginary Quadratic Fields Andrei Jorza Institute for Advanced Study December 16, 2010 To a regular algebraic cuspidal representation of GL(2) over a quadratic imaginary field, whose central character is conjugation invariant, Taylor et al. assoc
From playlist Mathematics
Open Quantum Kirwan Map - Guangbo Xu
Princeton/IAS Symplectic Geometry Seminar Topic: Open Quantum Kirwan Map Speaker: Guangbo Xu Affiliation: Visiting Professor, School of Mathematics Date: March 26, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Francis Brown - 3/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)
In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of
From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)
This lecture is part of an online graduate course on modular forms. We introduce modular forms, and give several examples of how they were used to solve problems in apparently unrelated areas of mathematics. I will not be following any particular book, but if anyone wants a suggestion
From playlist Modular forms
Symplectic forms in algebraic geometry - Giulia Saccà
Giulia Saccà Member, School of Mathematics January 30, 2015 Imposing the existence of a holomorphic symplectic form on a projective algebraic variety is a very strong condition. After describing various instances of this phenomenon (among which is the fact that so few examples are known!)
From playlist Mathematics
Maryna Viazovska: CM values of regularized theta lifts
Abstract: In this talk we will discuss arithmetic properties regularized Petersson products between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight 1 modular form with integral Fourier coefficients. We prove that such a Pet
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
p-adic modular forms - Christian Johansson
Short Talks by Postdoctoral Members Christian Johansson - September 29, 2015 http://www.math.ias.edu/calendar/event/88274/1443550500/1443551400 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members