Classical modular curve

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

Modular forms: Introduction

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: 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

John Voight: Computing classical modular forms as orthogonal modular forms

Abstract: Birch gave an extremely efficient algorithm to compute a certain subspace of classical modular forms using the Hecke action on classes of ternary quadratic forms. We extend this method to compute all forms of non-square level using the spinor norm, and we exhibit an implementatio

From playlist Algebraic and Complex Geometry

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: 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

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

Genus of abstract modular curves with level ℓℓ structure - Ana Cadoret

Ana Cadoret Ecole Polytechnique; Member, School of Mathematics November 21, 2013 To any bounded family of 𝔽ℓFℓ-linear representations of the etale fundamental of a curve XX one can associate families of abstract modular curves which, in this setting, generalize the `usual' modular curves w

From playlist Mathematics

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

Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields

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.

Héctor H. Pastén Vásquez: Shimura curves and bounds for the abc conjecture

Abstract: I will explain some new connections between the abc conjecture and modular forms. In particular, I will outline a proof of a new unconditional estimate for the abc conjecture, which lies beyond the existing techniques in this context. The proof involves a number of tools such as

From playlist Algebraic and Complex Geometry

Kalani Thalagoda - Bianchi modular forms

Bianchi Modular Forms are generalizations of classical modular forms for imaginary quadratic fields. Similar to the classical case, we can use the theory of modular symbols for computation. However, when the class group of the field is non-trivial, we can only compute certain components of

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

SummerSchool 20060804 1000 Darmon - Stark-Heegner points

From playlist Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry"

Shimura curves and new abc bounds -Hector Pasten

Joint IAS/Princeton University Number Theory Seminar Topic: Shimura curves and new abc bounds Speaker: Hector Pasten Affiliation: Harvard University Date: November 28, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

On the locally analytic vectors of the completed cohomology of modular curves - Lue Pan

Joint IAS/Princeton University Number Theory Seminar Topic: On the locally analytic vectors of the completed cohomology of modular curves Speaker: Lue Pan Affiliation: University of Chicago Date: October 22, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences

Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know

From playlist 2022 Summer School on the Langlands program

An overconvergent Eichler-Shimura map - Adrian Iovita

Adrian Iovita Corcordia University March 21, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

P-Adic Automorphic Forms and (big) Igusa Varieties by Sean Howe

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)

Francis Brown - 1/4 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: Fourier coefficients of Eisenstein series

This lecture is part of an online graduate course on modular forms. We calculate the Fourier coefficients of the Eisenstein series introduced in the previous lecture, and use them to construct the elliptic modular function. (Minor typo: in the definition of E10 I wrote 262 instead of 26

From playlist Modular forms