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
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Pythagorean Theorem VIII (Bhāskara's visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Bhāskara's proof (Behold!). This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #math #manim #
From playlist Pythagorean Theorem
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Pythagorean Theorem II (visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using a dissection of a square in two different ways. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #mathshort
From playlist Pythagorean Theorem
Negative moments of the Riemann zeta function - Alexandra Florea
50 Years of Number Theory and Random Matrix Theory Conference Topic: Negative moments of the Riemann zeta function Speaker: Alexandra Florea University of California, Irvine Date: June 23, 2022 I will talk about recent work towards a conjecture of Gonek regarding negative shifted moments
From playlist Mathematics
The recipe for moments of L-functions and characteristic polynomials of random mat... - Sieg Baluyot
50 Years of Number Theory and Random Matrix Theory Conference Topic: The recipe for moments of L-functions and characteristic polynomials of random matrices Speaker: Sieg Baluyot Affiliation: American Institute of Mathematics Date: June 23, 2022 In 2005, Conrey, Farmer, Keating, Rubinste
From playlist Mathematics
Unitary, Symplectic, and Orthogonal Moments of Moments - Emma Bailey
Analysis - Mathematical Physics Topic: Unitary, Symplectic, and Orthogonal Moments of Moments Speaker: Emma Bailey Affiliation: University of Bristol Date: November 15, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Statistics of the Zeros of the Zeta Function: Mesoscopic and Macroscopic Phenomena - Brad Rodgers
Brad Rodgers University of California, Los Angeles March 27, 2013 We review the well known microscopic correspondence between random zeros of the Riemann zeta-function and the eigenvalues of random matrices, and discuss evidence that this correspondence extends to larger mesoscopic collect
From playlist Mathematics
Opening Remarks and History of the math talks - Peter Sarnak, Hugh Montgomery and Jon Keating
50 Years of Number Theory and Random Matrix Theory Conference Topic: Opening Remarks and History of the math talks Speakers: Peter Sarnak, Hugh Montgomery and Jon Keating Date: June 21 2022
From playlist Mathematics
Proof: Supremum and Infimum are Unique | Real Analysis
If a subset of the real numbers has a supremum or infimum, then they are unique! Uniqueness is a tremendously important property, so although it is almost complete trivial as far as difficulty goes in this case, we would be ill-advised to not prove these properties! In this lesson we'll be
From playlist Real Analysis
Fermat's Last Theorem for rational and irrational exponents
Fermat's Last Theorem states the equation x^n + y^n = z^n has no integer solutions for positive integer exponents greater than 2. However, Fermat's Last Theorem says nothing about exponents that are not positive integers. Note: x, y and z are meant to be positive integers, which I should
From playlist My Maths Videos
Persi Diaconis: Haar-distributed random matrices - in memory of Elizabeth Meckes
Elizabeth Meckes spent many years studying properties of Haar measure on the classical compact groups along with applications to high dimensional geometry. I will review some of her work and some recent results I wish I could have talked about with her.
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Jon Keating: Random matrices, integrability, and number theory - Lecture 2
Abstract: I will give an overview of connections between Random Matrix Theory and Number Theory, in particular connections with the theory of the Riemann zeta-function and zeta functions defined in function fields. I will then discuss recent developments in which integrability plays an imp
From playlist Analysis and its Applications
Proof: Infimum of {1/n} = 0 | Real Analysis
The infimum of the set containing all reciprocals of natural numbers has an infimum of 0. That is, 0 is the greatest lower bound of {1/n | n is natural}. We prove this infimum in today's real analysis lesson using the Archimedean Principle, which tells us that given any real number x, we c
From playlist Real Analysis
In this video, we present a geometric proof of the Pythagorean theorem. This famous theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Our proof utilizes the prin
From playlist Shorts
Nina Snaith - Combining random matrix theory and number theory [2015]
Name: Nina Snaith Event: Program: Foundations and Applications of Random Matrix Theory in Mathematics and Physics Event URL: view webpage Title: Combining random matrix theory and number theory Date: 2015-10-14 @11:00 AM Location: 313 Abstract: Many years have passed since the initial su
From playlist Number Theory
A Q&A with our Kavli Medal & Lecture winner, Professor Henry Snaith
Professor Henry Snaith FRS answers questions from the audience at our recent Kavli Lecture. The lecture was recorded on April 26 2017 at the Royal Society. For more events like this, see our schedule - http://ow.ly/KhTi306gTN1
From playlist Latest talks and lectures
Applying the pythagorean formula to multiple triangles to find the missing length
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angl
From playlist Geometry - PYTHAGOREAN THEOREM
Kannan Soundararajan - 4/4 L-functions
Kannan Soundararajan - L-functions
From playlist École d'été 2014 - Théorie analytique des nombres