A nice basis for a nilpotent operator. Jordan basis. Jordan form for an operator on a finite-dimensional complex vector space.
From playlist Linear Algebra Done Right
Free ebook http://tinyurl.com/EngMath A short tutorial on how to apply Gauss' Divergence Theorem, which is one of the fundamental results of vector calculus. The theorem is stated and we apply it to a simple example.
From playlist Several Variable Calculus / Vector Calculus
In this video, I present the divergence theorem, which is a natural generalization of the fundamental theorem of calculus in 3 dimensions. It says that the surface integral of a vector field F is the triple integral of the divergence of F, and it provides a neat way of calculating surface
From playlist Multivariable Calculus
Kenichi Bannai - Shintani generating class and the p-adic polylogarithm for totally real fields
The organizer is sorry for the technical problem that a part of the slides is hidden. In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke L-functions for totally real fields. In particular, we will construct
From playlist Conférences Paris Pékin Tokyo
on the Brumer-Stark Conjecture (Lecture 2) by Samit Dasgupta
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Mahesh Kakde: Brumer-Stark units and a conjecture of Gross
The existence of Brumer-Stark unit is guaranteed by the Brumer-Stark conjecture. A conjecture of Dasgupta gives an explicit p-adic analytic formula for these units. An approach to this explicit formula is given by the tower of fields conjecture of Gross. After recalling these conjecture an
From playlist Number Theory
In this video we cover some rational function fundamentals, including asymptotes and interecepts.
From playlist Polynomial Functions
Claudia Alfes: Traces of CM values and geodesic cycle integrals of modular functions
In this talk we give an introduction to the study of generating series of the traces of CM values and geodesic cycle integrals of different modular functions. First we define modular forms and harmonic Maass forms. Then we briefly discuss the theory of theta lifts that gives a conceptual f
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
On the Gross—Stark conjecture 2 by Mahesh Kakde
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)
Explicit formulae for Gross-Stark units and Hilbert’s 12th problem by Mahesh Kakde
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
L'Hopital's Rule sine x over x
👉 Learn how to evaluate the limit of a function involving trigonometric expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The limit of a function is usually evaluated by direct
From playlist Evaluate Limits with Trig
Hajime Ishihara: The constructive Hahn Banach theorem, revisited
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: The Hahn-Banach theorem, named after the mathematicians Hans Hahn and Stefan Banach who proved it independently in the late 1920s, is a central tool in functional analys
From playlist Workshop: "Constructive Mathematics"
Matteo Longo: Half weight modular forms and rational points on elliptic curves
Let E be an elliptic curve, defined over the field of rational numbers, of conductor Np, where N is a positive integer and p is a prime which does not divide N. Let f be the weight 2 newform attached to E. We consider the Hida family passing through f. One can lift each classical form in t
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
On the Gross—Stark conjecture 1 by Mahesh Kakde
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)
Geometry-of-Numbers Techniques in Arithmetic Statistics (Lecture 3) by Arul Shankar
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,
From playlist Vector Calculus
Second ftc example with cube root
👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct
From playlist Evaluate Using The Second Fundamental Theorem of Calculus
Second FTC example with cube root
👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct
From playlist Evaluate Using The Second Fundamental Theorem of Calculus
The average size of 3-torsion in class groups of 2-extensions - Robert Lemke Oliver
\Joint IAS/Princeton University Number Theory Seminar Topic: The average size of 3-torsion in class groups of 2-extensions Speaker: Robert Lemke Oliver Affiliation: Tufts University Date: April 07, 2022 We determine the average size of the 3-torsion in class groups of G-extensions of a n
From playlist Mathematics