Betti's theorem

Stefaan Vaes: Cohomology and L2-Betti numbers for subfactors and quasi-regular inclusions

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 Analysis and its Applications

Matrix algebra: determinants | Appendix B2 | Fibonacci Numbers and the Golden Ratio

What is a the determinant of a matrix? Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1

From playlist Fibonacci Numbers and the Golden Ratio

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

Axioms of Lie algebra theory

In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi

From playlist Algebra

Theory of numbers: Fermat's theorem

This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se

From playlist Theory of numbers

Cassini's identity | Lecture 7 | Fibonacci Numbers and the Golden Ratio

Derivation of Cassini's identity, which is a relationship between separated Fibonacci numbers. The identity is derived using the Fibonacci Q-matrix and determinants. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pd

From playlist Fibonacci Numbers and the Golden Ratio

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

Triangle Inequality for Integrals of Complex Valued Functions | Complex Analysis

Twitter: https://twitter.com/meta_4_math Reddit: https://www.reddit.com/user/Meta4Math

From playlist Summer of Math Exposition Youtube Videos

Benjamini-Schramm Limits of Finite Volume Manifolds (Lecture-4) by Ian Biringer

PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE (ONLINE) ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Mahan M J (TIFR, Mumbai) DATE & TIME: 01 March 2021 to 12 March 2021 VENUE: Online Due to the ongoing COVID pandemic, the meeting will

From playlist Probabilistic Methods in Negative Curvature (Online)

Lewis Bowen - L2 invariants and Benjamini-Schramm convergence

October 30, 2015 - Princeton University Does there exist a sequence of free subgroups Fk of the isometry group of hyperbolic n-space such that the Cheeger constant of the quotient space Hn/Fk tends to zero as k tends to infinity? I will explain how to answer this (and related questions) w

From playlist Minerva Mini Course - Lewis Bowen

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

Colloquium MathAlp 2015 - Jean-Yves Welschinger

Polynômes aléatoires et topologie "Le lieu des zéros d'un polynôme à coefficients réels de n variables est (en général) une hypersurface de l'espace affine réel de dimension n dont la topologie dépend du choix du polynôme. À quelle topologie s'attendre lorsque le polynôme est choisi au ha

From playlist Colloquiums MathAlp

Joel Friedman - Sheaves on Graphs, L^2 Betti Numbers, and Applications.

Joel Friedman (University of British Columbia, Canada) Sheaf theory and (co)homology, in the generality developed by Grothendieck et al., seems to hold great promise for applications in discrete mathematics. We shall describe sheaves on graphs and their applications to (1) solving the

From playlist T1-2014 : Random walks and asymptopic geometry of groups.

An Amazing Connection Between the Riemann Hypothesis and Topology

https://gregoriousmaths.com/2021/08/19/a-couple-of-other-connections-between-number-theory-and-topology/ 0:00 Introduction and plan 2:32 The Riemann hypothesis 7:22 Introducing the complex we will study 19:41 Studying the asymptotic behaviour of \beta_k(\Delta_n) 22:54 Some number theoret

From playlist Summer of Math Exposition Youtube Videos

David Nadler: Betti Langlands in genus one

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 Algebraic and Complex Geometry

Francis Brown - 4/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)

In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of

From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)

Sarah Percival 7/27/22: Computation of Reeb Graphs in a Semi-Algebraic Setting

The Reeb graph is a tool from Morse theory that has recently found use in applied topology due to its ability to track changes in connectivity of level sets of a function. In this talk, I will motivate the use of semi-algebraic geometry as a setting for problems in applied topology and sho

From playlist AATRN 2022

Connections between classical and motivic stable homotopy theory - Marc Levine

Marc Levine March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu

From playlist Mathematics

Number Theorem | Gauss' Theorem

We prove Gauss's Theorem. That is, we prove that the sum of values of the Euler phi function over divisors of n is equal to n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Number Theory

Francis Brown - 2/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)

In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of

From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)