I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.
From playlist Differential Equations
Yilin Wang - 4/4 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is
From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory
C39 A Cauchy Euler equation that is nonhomogeneous
A look at what to do with a Cauchy Euler equation that is non-homogeneous.
From playlist Differential Equations
Yilin Wang - 3/3 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is
From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory
Yilin Wang - 1/4 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is
From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory
Yilin Wang - 2/4 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is
From playlist Yilin Wang - The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory
Differential Equations | Variation of Parameters.
We derive the general form for a solution to a differential equation using variation of parameters. http://www.michael-penn.net
From playlist Differential Equations
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
C38 Example problem solving a Cauchy Euler equation with initial values
Example problem solving a Cauchy-Euler equation with initial values.
From playlist Differential Equations
Eveliina Peltola (Bonn) -- On large deviations of SLEs and real rational functions
The talk concerns a large deviation principle (LDP) for (multiple) Schramm-Loewner evolution (SLE) curves for the Hausdorff metric. When studying the LDP, we introduced a ''Loewner potential'' that describes the rate function. This object turned out to have several intrinsic, and perhaps s
From playlist Columbia Probability Seminar
C36 Example problem solving a Cauchy Euler equation
An example problem of a homogeneous, Cauchy-Euler equation, with constant coefficients.
From playlist Differential Equations
C44 Example problem solving a Cauchy Euler equation
Getting more example problems done! Solving Cauchy-Euler equations is easy and fun.
From playlist Differential Equations
The Liouville conformal field theory quantum zipper - Morris Ang
Probability Seminar Topic: The Liouville conformal field theory quantum zipper Speaker: Morris Ang Affiliation: Columbia University Date: February 17, 2023 Sheffield showed that conformally welding a γ-Liouville quantum gravity (LQG) surface to itself gives a Schramm-Loewner evolution (
From playlist Mathematics
How to solve a differentialble equation by separating the variables
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Moments in positivity:metric positivity,covariance estimation,novel graph invariant by Apoorva Khare
ABSTRACT: I will discuss the connections of matrix positivity and its preservers to multiple sub-fields of mathematics: analysis, metric geometry, combinatorics, and also downstream applications. This includes classical results by Schur, Rudin, Loewner, Karlin, and their students: FitzGera
From playlist ICTS Colloquia
Conformal removability of non-simple Schramm-Loewner evolutions - Konstantinos Kavvadias
Probability Seminar Topic: Conformal removability of non-simple Schramm-Loewner evolutions Speaker: Konstantinos Kavvadias Affiliation: Tata Institute of Fundamental Research Date: April 07, 2023 We consider the Schramm-Loewner evolution (SLE_{kappa}) for kappa in (4,8), which is the re
From playlist Mathematics
Morris Ang (MIT) -- Integrability of the conformal loop ensemble
For κ between 8/3 and 8, the conformal loop ensemble CLEκ is a canonical random ensemble of loops which is conformally invariant in law, and whose loops locally look like Schramm-Loewner evolution with parameter κ. It describes the scaling limits of the Ising model, percolation, and other
From playlist Northeastern Probability Seminar 2021
Linear differential equations: how to solve
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to solve linear differential equations. In mathematics, linear differential equations are differential equations having differential equation solutions which can be added together to form other solutions.
From playlist A second course in university calculus.
Percolation: a Mathematical Phase Transition
—————SOURCES———————————————————————— Percolation – Béla Bollobás and Oliver Riordan Cambridge University Press, New York, 2006. Sixty Years of Percolation – Hugo Duminil-Copin https://www.ihes.fr/~duminil/publi/2018ICM.pdf Percolation – Geoffrey Grimmett volume 321 of Grundlehren der Ma
From playlist Prob and Stats