Siegel modular variety

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: 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: 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

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

Aaron Siegel - Polyformer: Generalized Enumeration of Polyforms - G4G13 April 2018

Polyformer is an extensible software toolkit for enumerating a wide variety of polyform types. The contribution is a paper describing polyformer and extensions to many OEIS polyform sequences. The software is open source and can be used to display arbitrary polyform sets and output STL fil

From playlist G4G13 Videos

Lynne Walling: Understanding quadratic forms on lattices through generalised theta series

Abstract: Siegel introduced generalised theta series to study representation numbers of quadratic forms. Given an integral lattice L with quadratic form q, Siegel’s degree n theta series attached to L has a Fourier expansion supported on n-dimensional lattices, with Fourier coefficients th

From playlist Women at CIRM

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 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

An Euler system for genus 2 Siegel modular forms - David Loeffler

Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: An Euler system for genus 2 Siegel modular forms Speaker: David Loeffler Affiliation: University of Warwick Date: November 8, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Jacob Lurie - Tamagawa Numbers and Nonabelian Poincare Duality, I [2013]

Jacob Lurie Wednesday, August 28 3:10PM Tamagawa Numbers and Nonabelian Poincare Duality, I Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: Let q and q0 be positive definite integral quadratic forms. We say that

From playlist Number Theory

Sophie Morel - Shimura Varieties (3/3)

Depending on your point of view, Shimura varieties are a special kind of locally symmetric spaces, a generalization of moduli spaces of abelian schemes with extra structures, or the imperfect characteristic 0 version of moduli spaces of shtuka. They play an important role in the Langlands

From playlist 2022 Summer School on the Langlands program

Modular forms: Classification

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

Standard L-functions and theta correspondence by Shunsuke Yamana

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

Jacob Tsimerman, Unlikely intersections and the André-Oort conjecture

VaNTAGe Seminar, December 7, 2021 License: CC-BY-NC-SA

From playlist Complex multiplication and reduction of curves and abelian varieties

The Theta Correspondence Origins, Results, and Ramifications Part I

Professor Roger Howe, Texas A&M University, USA

From playlist Distinguished Visitors Lecture Series

Standard L-functions and theta correspondence (Lecture 2) by Shunsuke Yamana

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

Marc Hindry: Brauer-Siegel theorem and analogues for varieties over global fields

Abstract: The classical Brauer-Siegel theorem can be seen as one of the first instances of description of asymptotical arithmetic: it states that, for a family of number fields Ki, under mild conditions (e.g. bounded degree), the product of the regulator by the class number behaves asympt

From playlist Algebraic and Complex Geometry

Hodge theory and algebraic cycles - Phillip Griffiths

Geometry and Arithmetic: 61st Birthday of Pierre Deligne Phillip Griffiths Institute for Advanced Study October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a f

From playlist Pierre Deligne 61st Birthday

Number Theory | Modular Inverses: Example

We give an example of calculating inverses modulo n using two separate strategies.

From playlist Modular Arithmetic and Linear Congruences