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 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 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 | 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
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
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
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
Modular forms: Theta functions
This lecture is part of an online graduate course on modular forms. We show that the theta function of a 1-dimensional lattice is a modular form using the Poisson summation formula, and use this to prove the functional equation of the Riemann zeta function. For the other lectures in th
From playlist Modular forms
Modular forms: Theta functions in higher dimensions
This lecture is part of an online graduate course on modular forms. We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors
From playlist Modular forms
Dyson's Rank, Harmonic Weak Maass Form, and Recent Developments - Kathrin Bringmann
Kathrin Bringmann University of Cologne September 27, 2013 More videos on http://video.ias.edu
From playlist Dreams of Earth and Sky
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
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
Michael Harris: Construction of p-adic L-functions for unitary groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
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
Sander Zwegers: Fourier coefficients of meromorphic Jacobi forms
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 2
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Modular forms and multiple q-Zeta values (Lecture 2) by Ulf Kuehn
PROGRAM : ALGEBRAIC AND ANALYTIC ASPECTS OF AUTOMORPHIC FORMS ORGANIZERS : Anilatmaja Aryasomayajula, Venketasubramanian C G, Jurg Kramer, Dipendra Prasad, Anandavardhanan U. K. and Anna von Pippich DATE & TIME : 25 February 2019 to 07 March 2019 VENUE : Madhava Lecture Hall, ICTS Banga
From playlist Algebraic and Analytic Aspects of Automorphic Forms 2019
Conformal Limits of Parabolic Higgs Bundles by Richard Wentworth
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
B. Deroin - Monodromy of algebraic families of curves (Part 2)
The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Modularity in Weight (1,1,...,1) via Overconvergent Hilbert Modular Forms - Payman Kassaei
Payman Kassaei March 29, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics