The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Calculus - The Fundamental Theorem, Part 2
The Fundamental Theorem of Calculus. A discussion of the antiderivative function and how it relates to the area under a graph.
From playlist Calculus - The Fundamental Theorem of Calculus
A Converse to a Theorem of Gross-Zaqier-Kolyvagin - Christopher Skinner
Christopher Skinner Princeton University; Member, School of Mathematics April 4, 2013 The theorem of the title is that if the L-function L(E,s) of an elliptic curve E over the rationals vanishes to order r=0 or 1 at s=1 then the rank of the group of rational rational points of E equals r a
From playlist Mathematics
Calculus - The Fundamental Theorem, Part 3
The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.
From playlist Calculus - The Fundamental Theorem of Calculus
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
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Sasha Sodin (QMUL) -- A random operator constructed from representations (Part 1)
We shall discuss the construction of an amusing random operator acting on certain representations of the infinite symmetric group and sharing some features with the Anderson model. Particularly, we show that the spectrum of the operator exhibits so-called quantum Lifshitz tails, characteri
From playlist Integrable Probability Working Group
Quasi-periodic solutions to nonlinear PDE's - Wei-Min Wang
Analysis Seminar Topic: Quasi-periodic solutions to nonlinear PDE's Speaker:Wei-Min Wang Affiliation: Université Paris-Sud Date: October 26, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Stable Homotopy Seminar, 15: Dualizable and invertible spectra
I present the useful fact that spectra are generated by finite complexes under filtered homotopy colimits. I then define Spanier-Whitehead duality, which is a special case of a notion of duality that exists in any closed symmetric monoidal category. Two natural classes of spectra rise from
From playlist Stable Homotopy Seminar
Spin Glass Phase at Zero Temperature in the Edwards--Anderson Model by Sourav Chatterjee
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY
Calculus - The Fundamental Theorem, Part 5
The Fundamental Theorem of Calculus. How an understanding of an incremental change in area helps lead to the fundamental theorem
From playlist Calculus - The Fundamental Theorem of Calculus
David Jerison: Localization of eigenfunctions via an effective potential
Abstract: We discuss joint work with Doug Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda. Consider the Neumann boundary value problem for the operator L=divA∇+V on a Lipschitz domain Ω and, more generally, on manifolds with and without boundary. The eigenfunctions of L are often
From playlist Mathematical Physics
The solution of the Kadison-Singer problem - Daniel Spielman
Daniel Spielman Yale University November 5, 2014 We will explain our recent solution of the Kadison-Singer Problem and the equivalent Bourgain-Tzafriri and Paving Conjectures. We will begin by introducing the method of interlacing families of polynomials and use of barrier function argume
From playlist Mathematics
Self-organized criticality and marginality in Ising spin glasses by Auditya Sharma
Indian Statistical Physics Community Meeting 2018 DATE:16 February 2018 to 18 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community which is attended by scientists, postdoctoral fellows, and graduate s
From playlist Indian Statistical Physics Community Meeting 2018
Mathematical Research Lecture -- Kyle Broder -- Curvature and Moduli
A recent talk I gave concerning the link between the curvature of the total space of a family of compact complex manifolds and the moduli-theoretic behaviour of the fibres. Part of this research appears in my Ph.D. thesis, and will appear in an upcoming preprint. 💪🙏 Support the channel b
From playlist Research Lectures
Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.
From playlist Physics ONE
Quasiperiodic Schroedinger Operators with Multiple Frequencies - Wilhelm Schlag
Analysis and Beyond - Celebrating Jean Bourgain's Work and Impact May 23, 2016 More videos on http://video.ias.edu
From playlist Analysis and Beyond