Modular forms

Hecke operator

In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by Erich Hecke, is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations. (Wikipedia).

Video thumbnail

呼叫魚

好恐佈,咁都食得落口

From playlist Crazy Stuff

Video thumbnail

the Internet (part 2)

An intro to the core protocols of the Internet, including IPv4, TCP, UDP, and HTTP. Part of a larger series teaching programming. See codeschool.org

From playlist The Internet

Video thumbnail

20 AWESOME Electromagnetic induction in laboratory!!!

This videos shoe and describes about the Electromagnetic Induction, Faraday's observation.It also describes about the magnitude and direction of induced e.m.f, Faraday’s Laws of Electromagnetic Induction and the Lenz’s Law.

From playlist ELECTROMAGNETISM

Video thumbnail

Arthur's trace formula and distribution of Hecke eigenvalues for GL(n) - Jasmin Matz

Jasmin Matz Member, School of Mathematics February 23, 2015 A classical problem in the theory of automorphic forms is to count the number of Laplace eigenfunctions on the quotient of the upper half plane by a lattice LL. For LL a congruence subgroup in SL(2,ℤ)SL(2,Z) the Weyl law was prov

From playlist Mathematics

Video thumbnail

C35 The Cauchy Euler Equation

I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.

From playlist Differential Equations

Video thumbnail

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

Video thumbnail

The geometric theory of automorphic...possible surprises I - Robert Langlands

Beyond Endoscopy Topic: The geometric theory of automorphic forms over Riemann surfaces as a theory of eigenfunctions of Hecke operators and its possible surprises I Speaker: Robert Langlands, Professor Emeritus, School of Mathematics Time/Room: 10:45am - 11:35am/S-101 More videos on htt

From playlist Mathematics

Video thumbnail

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

Video thumbnail

Ken Ribet, Ogg's conjecture for J0(N)

VaNTAGe seminar, May 10, 2022 Licensce: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Mazur: http://www.numdam.org/article/PMIHES_1977__47__33_0.pdf Ogg: https://eudml.org/doc/142069 Stein Thesis: https://wstein.org/thesis/ Stein Book: https://wstein.org/books/modform/s

From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)

Video thumbnail

Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 4

In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly

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

Video thumbnail

Mark W. McConnell: Computing Hecke operators for cohomology of arithmetic subgroups of SL_n(Z)

Abstract: We will describe two projects. The first which is joint with Avner Ash and Paul Gunnells, concerns arithmetic subgroups Γ of G=SL_4(Z). We compute the cohomology of Γ∖G/K, focusing on the cuspidal degree H^5. We compute a range of Hecke operators on this cohomology. We fi Galois

From playlist Number Theory

Video thumbnail

Matt Hogancamp: Soergel bimodules and the Carlsson-Mellit algebra

The dg cocenter of the category of Soergel bimodules in type A, morally speaking, can be thought of as a categorical analogue of the ring of symmetric functions, as in joint work of myself, Eugene Gorsky, and Paul Wedrich. Meanwhile, the ring of symmetric functions is the recipient of acti

From playlist Workshop: Monoidal and 2-categories in representation theory and categorification

Video thumbnail

Computations in the topology of locally symmetric spaces -Mark McConnell

Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Computations in the topology of locally symmetric spaces Speaker: Mark McConnell Affiliation: Princeton University Date: November 8, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

B03 An improvement of the Euler method

Introducing predictor-corrector methods, improving on Euler's method of numerical analysis.

From playlist A Second Course in Differential Equations

Video thumbnail

“Computational methods for modular and Shimura curves,” by John Voight (Part 7 of 8)

“Computational methods for modular and Shimura curves,” by John Voight (Dartmouth College). The classical method of modular symbols on modular curves is introduced to compute the action of the Hecke algebra and corresponding spaces of modular forms. Generalizations to Shimura curves will t

From playlist CTNT 2016 - “Computational methods for modular and Shimura curves" by John Voight

Related pages

Petersson inner product | Modular group | Upper half-plane | Multiplicative function | Vector space | Self-adjoint operator | Ramanujan tau function | Lattice (group) | Spectral theorem | Euler product | Hecke algebra (disambiguation) | Modular form | Determinant | Eichler–Shimura congruence relation | Double coset | Mellin transform | Homogeneous function | Group ring | Modular curve | Braid group | Cusp form | Mathematics | Eigenform | Wiles's proof of Fermat's Last Theorem | Hecke algebra | Eigenfunction | Subgroup | Abstract algebra | Analytic function | Dirichlet series | Harmonic analysis | Commutative ring