Conjectures that have been proved | Topology
The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. The conjectures, formulated by Kiiti Morita in 1976, asked 1. * If is normal for every normal space Y, is X a discrete space? 2. * If is normal for every normal P-space Y, is X metrizable? 3. * If is normal for every normal countably paracompact space Y, is X metrizable and sigma-locally compact? The answers were believed to be affirmative. Here a normal P-space Y is characterised by the property that the product with every metrizable X is normal; thus the conjecture was that the converse holds. Keiko Chiba, Teodor C. Przymusiński, and Mary Ellen Rudin proved conjecture (1) and showed that conjectures (2) and (3) cannot be proven false under the standard ZFC axioms for mathematics (specifically, that the conjectures hold under the axiom of constructibility V=L). Fifteen years later, Zoltán Tibor Balogh succeeded in showing that conjectures (2) and (3) are true. (Wikipedia).
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
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
An Analogue of the Ichino-Ikeda Conjecture for... coefficients of the Metaplectic Group - Erez Lapid
Erez Lapid Hebrew University of Jerusalem and Weizmann Institute of Science March 14, 2013 A few years ago Ichino-Ikeda formulated a quantitative version of the Gross-Prasad conjecture, modeled after the classical work of Waldspurger. This is a powerful local-to-global principle which is
From playlist Mathematics
Nobuo Sato: Charlton's conjecture on multiple zeta values
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: In this talk, we give a proof of the generalized cyclic insertion conjecture on the MZVs, which was formulated by Steven Charlton in his thesi
From playlist Workshop: "Periods and Regulators"
Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers
#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require
From playlist MegaFavNumbers
Why science is NOT 'Just a Theory'
Have you ever heard ‘evolution’ dismissed as ‘just a theory’? Is a scientific theory no different to the theory that Elvis is still alive? Jim Al-Khalili puts the record straight. Subscribe for regular science videos: http://bit.ly/RiSubscRibe There’s an important difference between a sci
From playlist Ri Animations
The Generalized Ramanujan Conjectures and Applications - Lecture 1 by Peter Sarnak
Lecture 1: The Generalized Ramanujan Conjectures Abstract: One of the central problems in the modern theory of automorphic forms is the Generalized Ramanujan Conjecture.We review the development and formulation of these conjectures as well as recent progress. While the general Conjecture
From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak
Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► https
From playlist Geometry
Broué’s Abelian Defect Group Conjecture I - Jay Taylor
Seminar on Geometric and Modular Representation Theory Topic: Broué’s Abelian Defect Group Conjecture I Speaker: Jay Taylor Affiliation: University of Southern California; Member, School of Mathematics Date: September 9, 2020 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Ulrich Bunke: Coarse homotopy theory and K-theory
Talke by Ulrich Bundle in Global Noncommutative Geometry Seminar (Americas) on September 30, 2022. https://globalncgseminar.org/talks/tba-36/
From playlist Global Noncommutative Geometry Seminar (Americas)
Overview of null hypothesis, examples of null and alternate hypotheses, and how to write a null hypothesis statement.
From playlist Hypothesis Tests and Critical Values
Rationality and Morita equivalence for blocks of finite groups by Radha Kessar
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Macdonald polynomials and decomposition numbers for finite unitary groups - Olivier Dudas
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Macdonald polynomials and decomposition numbers for finite unitary groups Speaker: Olivier Dudas Affiliation: Institut de mathématiques de Jussieu–Paris Rive Gauche Date: November 20, 2020 For more video pl
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Broué’s Abelian Defect Group Conjecture II - Daniel Juteau
Seminar on Geometric and Modular Representation Theory Topic: Broué’s Abelian Defect Group Conjecture II Speaker: Daniel Juteau Affiliation: Centre National de la Recherche Scientifique/Université Paris Diderot; Member, School of Mathematics Date: September 16, 2020 For more video please
From playlist Seminar on Geometric and Modular Representation Theory
Paulo Carrillo Rouse: Chern assembly map for discrete groups and index theory
Talk by Paulo Carrillo Rouse in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on April 14, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Broué’s Abelian Defect Group Conjecture II - Daniel Juteau
Seminar on Geometric and Modular Representation Theory Topic: Broué’s Abelian Defect Group Conjecture II Speaker: Daniel Juteau Affiliation: Centre National de la Recherche Scientifique/Université Paris Diderot; Member, School of Mathematics Date: September 16, 2020 For more video please
From playlist Seminar on Geometric and Modular Representation Theory
Francesca Arici: Sphere bundles in noncommutative geometry
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Cuntz-Pimsner algebras are universal C*-algebras associated to a C*-correspondence and they encode dynamical information. In the case of a self Morita equivalence bimodule they can b
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Most paradoxes either stem from the misunderstanding of a topic, or aren't really paradoxes. However, here is a paradox that seems to contradict logic itself. What's going on here? And what does the liar paradox have to do with computer science? #some2
From playlist Summer of Math Exposition 2 videos