Quantum Integral. Gauss would be proud! I calculate the integral of x^2n e^-x^2 from -infinity to infinity, using Feynman's technique, as well as the Gaussian integral and differentiation. This integral appears over and over again in quantum mechanics and is useful for calculus and physics
From playlist Integrals
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Patrick Ingram, The critical height of an endomorphism of projective space
VaNTAGe seminar on June 9, 2020. License: CC-BY-NC-SA. Closed captions provided by Matt Olechnowicz
From playlist Arithmetic dynamics
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
Euler-Mascheroni VI: An Integral Representation of the Harmonic Numbers
Channel social media: Instagram: @whatthehectogon https://www.instagram.com/whatthehect... Twitter: @whatthehectogon https://twitter.com/whatthehectogon Any questions? Leave a comment below or email me at the misspelled whatthehectagon@gmail.com In this video, I prepare my next barrag
From playlist Analysis
Millennium Maths Problems Explained in 90 Seconds
All 7 Millennium Maths Problems explained in 90 seconds by Oxford Mathematician Dr Tom Crawford. The Millennium Prize Problems are a set of unsolved maths questions which each have a $1-million reward for a successful solution courtesy of the Clay Math Institute. They are seen by many as s
From playlist Director's Cut
Projective structures on Riemann surfaces and their monodromy by Subhojoy Gupta
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Symplectic Dynamics of Integrable Hamiltonian Systems - Alvaro Pelayo
Alvaro Pelayo Member, School of Mathematics April 4, 2011 I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian
From playlist Mathematics
Sergey Fomin: Morsifications and mutations
Abstract: I will discuss a connection between the topology of isolated singularities of plane curves and the mutation equivalence of the quivers associated with their morsifications. Joint work with Pavlo Pylyavskyy, Eugenii Shustin, and Dylan Thurston. Recording during the thematic meeti
From playlist Topology
Nathan Dunfield, Lecture 2: A Tale of Two Norms
33rd Workshop in Geometric Topology, Colorado College, June 10, 2016
From playlist Nathan Dunfield: 33rd Workshop in Geometric Topology
How many revolutions on this Ellipse?
How many revolutions on this Pythagorean ellipse? Suppose an ellipse rolls over a sine curve in such a way that one revolution of the ellipse equals to one period of the curve, how are the axes of the ellipse related to the amplitude. The answer is surprisingly related to the Pythagorean t
From playlist Calculus
A series involving harmonic numbers. Featuring the dilogarithm function.
We use generating functions to calculate the sum of an interesting series involving harmonic numbers. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Dilogarithm
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
Jessica Purcell - Lecture 3 - Knots in infinite volume 3-manifolds
Jessica Purcell, Monash University Title: Knots in infinite volume 3-manifolds Classically, knots have been studied in the 3-sphere. However, many examples of knots arising in applications lie in broader classes of 3-manifolds. These include virtual knots, which lie within thickened surfa
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
From Embedded Contact Homology to Surface Dynamics - Jo Nelson
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: From Embedded Contact Homology to Surface Dynamics Speaker: Jo Nelson Affiliation: Rice University; Member, School of Mathematics Date: February 27 2023 I will discuss work in progress with Morgan Weiler on knot filtered e
From playlist Mathematics
logarithm of a matrix. I calculate ln of a matrix by finding the eigenvalues and eigenvectors of that matrix and by using diagonalization. It's a very powerful tool that allows us to find exponentials, sin, cos, and powers of a matrix and relates to Fibonacci numbers as well. This is a mus
From playlist Eigenvalues
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
IGA: Luca di Cerbo - The Singer conjecture in dimension three revisited and its extensions
Abstract: In this talk, I will show how Price inequalities for harmonic forms combined with some standard topology and geometry of 3-manifolds imply the Singer conjecture in dimension three. This provides an alternative proof of a result of Lott and Lueck (Invent. Math., 1995). Finally, I
From playlist Informal Geometric Analysis Seminar