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 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
Discrete Structures: Modular arithmetic
A review of modular arithmetic. Congruent values; addition; multiplication; exponentiation; additive and multiplicative identity.
From playlist Discrete Structures
Modular Arithmetic: Under the Hood
Modular arithmetic visually! For aspiring mathematicians already familiar with modular arithmetic, this video describes how to formalize the concept mathematically: to define the integers modulo n, to define the operations of addition and multiplication, and check that these are well-def
From playlist Modular Arithmetic Visually
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
Glenn STEVENS - Modular Symbols, K-theory, and Eisenstein Cohomology
In this talk we will give an adelic construction of an object that we call the Kato-Beilinson modular symbol for GL(2), extending constructions of Goncharov and Brunault. We obtain a modular symbol Ψbelonging to the compactly supported cohomology of arithmetic subgroups of GL(2
From playlist Mathematics is a long conversation: a celebration of Barry Mazur
Petru Constantinescu - On the distribution of modular symbols and cohomology classes
Motivated by a series of conjectures of Mazur, Rubin and Stein, the study of the arithmetic statistics of modular symbols has received a lot of attention in recent years. In this talk, I will highlight several results about the distribution of modular symbols, including their Gaussian dist
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
“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
“Computational methods for modular and Shimura curves,” by John Voight (Part 6 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
Introduction To Beilinson--Kato Elements And Their Applications 2 by Chan-Ho Kim
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
Modular symbols and arithmetic II - Romyar Sharifi
Locally Symmetric Spaces Seminar Topic: Modular symbols and arithmetic II Speaker: Romyar Sharifi Affiliation: University of California; Member, School of Mathematics Date: January 30, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
“Computational methods for modular and Shimura curves,” by John Voight (Part 4 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
“Computational methods for modular and Shimura curves,” by John Voight (Part 5 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
Lec 5 | MIT 6.033 Computer System Engineering, Spring 2005
Fault Isolation with Clients and Servers View the complete course at: http://ocw.mit.edu/6-033S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.033 Computer System Engineering, Spring 2005
Stark-Heegner cycles for Bianchi modular forms by Guhan Venkat
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Modular arithmetic visually! We use a visualization tool called a "dynamical portrait." We explore addition and multiplication modulo n, and discover and prove the portrait is made of cycles if and only if the function (f(z) = z+a mod n or f(z) = az mod n) is bijective. This treatment
From playlist Modular Arithmetic Visually
