Everything You Need to Know About Control Theory
Control theory is a mathematical framework that gives us the tools to develop autonomous systems. Walk through all the different aspects of control theory that you need to know. Some of the concepts that are covered include: - The difference between open-loop and closed-loop control - How
From playlist Control Systems in Practice
Boris Adamczewski: Mahler's method in several variables
Abstract: Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number
From playlist Combinatorics
Ziyang Gao - Number of Points on Curves: a Conjecture of Mazur
With Philipp Habegger we recently proved a height inequality, using which one can bound the number of rational points on 1-parameter families of curves in terms of the genus, the degree of the number field and the Mordell-Weil rank (but no dependence on the Faltings height). This gives an
From playlist Journée Gretchen & Barry Mazur
The Routh-Hurwitz Stability Criterion
In this video we explore the Routh Hurwitz Stability Criterion and investigate how it can be applied to control systems engineering. The Routh Hurwitz Stability Criterion can be used to determine how many roots of a polynomial are in the right half plane. Topics and time stamps: 0:00 –
From playlist Control Theory
Olivier Glass : Control of the motion of a set of particles
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Control Theory and Optimization
We show the connection between the method of adjoints in optimal control to the implicit function theorem ansatz. We relate the costate or adjoint state variable to Lagrange multipliers.
From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)
Cayley-Hamilton Theorem [Control Bootcamp]
Here we describe the Cayley-Hamilton Theorem, which states that every square matrix satisfies its own characteristic equation. This is very useful to prove results related to controllability and observability. These lectures follow Chapter 8 from: "Data-Driven Science and Engineering: Ma
From playlist Control Bootcamp
Lyapunov Stability via Sperner's Lemma
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of i
From playlist Summer of Math Exposition Youtube Videos
VaNTAGe seminar, on Sep 15, 2020 License: CC-BY-NC-SA.
From playlist Rational points on elliptic curves
Transfer Functions: Introduction and Implementation
In this video we introduce transfer functions and show how they can be derived from a set of linear, ordinary differential equations. We also examine how to use a transfer function to predict the output of system to a given input. Topics and time stamps: 0:38 – Example using an aircraft
From playlist Control Theory
Ken Ribet, Ogg's conjecture for J0(N)
VaNTAGe seminar, May 10, 2022 Licensce: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Mazur: http://www.numdam.org/article/PMIHES_1977__47__33_0.pdf Ogg: https://eudml.org/doc/142069 Stein Thesis: https://wstein.org/thesis/ Stein Book: https://wstein.org/books/modform/s
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
How does the rank of an elliptic curve grow in towers of number fields? - Florian Sprung
Joint IAS/Princeton University Number Theory Seminar Topic: How does the rank of an elliptic curve grow in towers of number fields? Speaker: Florian Sprung Affiliation: Arizona State University Date: April 18, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Recovering elliptic curves from their p-torsion - Benjamin Bakker
Benjamin Bakker New York University May 2, 2014 Given an elliptic curve EE over a field kk, its p-torsion EpEp gives a 2-dimensional representation of the Galois group GkGk over 𝔽pFp. The Frey-Mazur conjecture asserts that for k=ℚk=Q and p13p13, EE is in fact determined up to isogeny by th
From playlist Mathematics
Quantifying Eisenstein congruences - Preston Wake
Short talks by postdoctoral members Topic:Quantifying Eisenstein congruences Speaker: Preston Wake Affiliation: Member, School of Mathematics Date: Oct 5, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Ekin Ozman, Quadratic points on modular curves and Fermat-type equations
VaNTAGe seminar, June 8, 2021 License: CC-BY-NC-SA
From playlist Modular curves and Galois representations
Derived structures controlling representations - Carl Wang-Erickson
More videos on http://video.ias.edu
From playlist Mathematics
Joseph Silverman, Moduli problems and moduli spaces in algebraic dynamics
VaNTAGe seminar on June 23, 2020. License: CC-BY-NC-SA. Closed captions provided by Max Weinreich
From playlist Arithmetic dynamics
CurvesSurfaces3: De Casteljau Bezier Curves in Algebraic Calculus | N J Wildberger
We explain how to extend Archimedes' famous Parabolic Area Formula to the cubic situation. This formula was historically the first major calculation in Calculus, and gave an explicit and workable formula for the area of a slice of a parabola, cut off by a chord, in terms of the area of a p
From playlist MathSeminars