(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
The Lawvere fixed point theorem
In this video we prove a version of Lawveres fixed point theorem that holds in Cartesian closed categories. It's a nice construction that specializes to results such as Cantors diagonal argument and prove the the power set of a set is classically always larger than the set itself. https:/
From playlist Logic
This lecture is part of an online course on Galois theory. This is an introductory lecture, giving an informal overview of Galois theory. We discuss some historical examples of problems that it was used to solve, such as the Abel-Ruffini theorem that degree 5 polynomials cannot in genera
From playlist Galois theory
Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy
Balazs Szegedy University of Toronto; Member, School of Mathematics October 4, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large comp
From playlist Mathematics
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy
Balazs Szegedy University of Toronto; Member, School of Mathematics October 11, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large com
From playlist Mathematics
Mr LIMA de CARVALHO e SILVA - From Essential Inclusions to Local Geometric Morphisms
It is well known that, given a site of denition, a subtopos of Grothendieck topos can be obtained by strengthening the Grothendieck topology, thus obtaining an inclusion of toposes. An essential inclusion is one where the inverse image functor of this inclusion has a left adjoint. Kelly an
From playlist Topos à l'IHES
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
Paul André Melliès: Refinement type systems and Martin Lof type theory
Please Note: Due to technical issues the recordings of the blackboard are shown in a slideshow manner. The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In this talk, I will review my recent work with Noam Zeilberger on
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
What A General Diagonal Argument Looks Like (Category Theory)
Diagonal Arguments are a powerful tool in maths, and appear in several different fundamental results, like Cantor's original Diagonal argument proof (there exist uncountable sets, or "some infinities are bigger than other infinities"), Turing's Halting Problem, Gödel's incompleteness theor
From playlist Summer of Math Exposition 2 videos
Model Theory - part 02 - Signatures, Lawvere Categories, Structures (now valued in Categories!)
I learned about this approach from Riehl in the existential context here. Her webpage is here: http://www.math.jhu.edu/~eriehl/ Also, I found the refrences by Caramello and Awodey very helpful. They build on what is done in Reyes-Makkai. Whatever Awodey writes is basically gold. Here he
From playlist Model Theory
Giuseppe Rosolini: Quotient completions and applications
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: The notion of elementary quotient completion of a Lawvere elementary doctrine introduced by Maietti and Rosolini proved to be a generalization of the notion of the exact
From playlist Workshop: "Proof, Computation, Complexity"
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
A review of the notes common to all formations of a G chord.
From playlist Music Lessons
Laurent Lafforgue - 4/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Laurent Lafforgue - 2/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Laurent Lafforgue - 3/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
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