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
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
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
When do fractional differential equations have maximal solutions?
When do fractional differential equations have maximal solutions? This video discusses this question in the following way. Firstly, a comparison theorem is formulated that involves fractional differential inequalities. Secondly, a sequence of approximative problems involving polynomials
From playlist Research in Mathematics
Alexander Volberg: From harmonic analysis problems to Hamilton-Jacobi-Bellman PDE and back (2)
We will explain the Bellman function approach to some singular integral estimates. There is a dictionary that translates the language of singular integrals to the language of stochastic optimization. The main tool in stochastic optimization is a Hamilton-Jacobi-Bellman PDE. We show how thi
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
Applications of analysis to fractional differential equations
I show how to apply theorems from analysis to fractional differential equations. The ideas feature the Arzela-Ascoli theorem and Weierstrass' approximation theorem, leading to a new approach for solvability of certain fractional differential equations. When do fractional differential equ
From playlist Mathematical analysis and applications
Ahlfors-Bers 2014 "Computing the image of Thurston's skinning map"
David Dumas (UIC): Thurston's skinning map is a holomorphic map between Teichmüller spaces that arises in the construction of hyperbolic structures on compact 3-manifolds. I will describe the theory and implementation of a computer program that computes the images of skinning maps in some
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Joe Neeman: Gaussian isoperimetry and related topics III
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal... - Laura Cladek
Analysis & Mathematical Physics Topic: Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal Uncertainty Principle Speaker: Laura Cladek Affiliation: von Neumann Fellow, School Of Mathematics Date: December 14, 2022 We obtain new bounds on the additive energy
From playlist Mathematics
Ahlfors-Bers 2014 "Quasi-isometric rigidity of the class of convex-cocompact Kleinian groups"
Peter Haïssinsky (Toulouse): The talk will be devoted to discussing background and ingredients for the proof of the following theorem: a finitely generated group quasi-isometric to a convex-cocompact Kleinian group contains a finite index subgroup isomorphic to a convex-cocompact Kleinian
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
On the dyadic Hilbert transform – Stefanie Petermichl – ICM2018
Analysis and Operator Algebras Invited Lecture 8.10 On the dyadic Hilbert transform Stefanie Petermichl Abstract: The Hilbert transform is an average of dyadic shift operators. These can be seen as a coefficient shift and multiplier in a Haar wavelet expansion or as a time shifted operat
From playlist Analysis & Operator Algebras
Ahlfors-Bers 2014 "Roots of Polynomials and Parameter Spaces"
Sarah Koch (University of Michigan): In his last paper, "Entropy in Dimension One," W. Thurston completely characterized which algebraic integers arise as exp(entropy(f)), where f is a postcritically finite real map of a closed interval. On page 1 of this paper, there is a spectacular ima
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Ahlfors-Bers 2014 "Surface Subgroups, Cube Complexes, and the Virtual Haken Theorem"
Jeremy Kahn (CUNY Graduate Center): In a largely expository talk, I will summarize the results leading up to the Virtual Haken and Virtual Fibered Theorem for three manifolds, including 1. The Geometrization Theorem of Thurston and Perelman 2. The Surface Subgroup Theorem of the speaker an
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude. #math #geometry #mtbos #manim #animation #theorem #pww #proofwith
From playlist MathShorts
Ahlfors Bers 2014 "The complex geometry of Teichmüller space and symmetric domains"
Stergios Antonakoudis (Cambridge University): From a complex analytic perspective, Teichmüller spaces can be realized as contractible bounded domains in complex vector spaces by the Bers embeddings. Bounded Symmetric domains constitute another class of bounded domains that has been extensi
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Evaluating Limits Definition of Derivative
I work through 2 example evaluating the limit definition of a derivative. Check out http://www.ProfRobBob.com, there you will find my lessons organized by chapters within each subject. If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my chann
From playlist Calculus (New)
J.-M. Martell - A minicourse on Harmonic measure and Rectifiability (Part 3)
Solving the Dirichlet boundary value problem for an elliptic operator amounts to study the good properties of the associated elliptic measure. In the context of domains having an Ahlfors regular boundary and satisfying theso-called interior corkscrew and Harnack chain conditions (these ar
From playlist Rencontres du GDR AFHP 2019
Simplifying the difference quotient of a quadratic function
👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
From playlist Evaluate the Limit (PC)
Are math people elitist? Do you think this is true? I discuss this and I also talk about four famous math books which are considered extremely rigorous. The books are Real and Complex Analysis by Rudin which is also known as "Papa Rudin", Principles of Mathematical Analysis by Rudin which
From playlist Book Reviews