Metric geometry | Dimension theory | Measure theory | Unsolved problems in geometry | Conjectures
In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact -dimensional spaces. Intuitively, it states that a set of points that is large in its Hausdorff dimension must determine a set of distances that is large in measure. More precisely, if is a compact set of points in -dimensional Euclidean space whose Hausdorff dimension is strictly greater than , then the conjecture states that the set of distances between pairs of points in must have nonzero Lebesgue measure. (Wikipedia).
Falconer distance set problem - Hong Wang
Short Talks by Postdoctoral Members Topic: Falconer distance set problem Speaker: Hong Wang Affiliation: Member, School of Mathematics Date: September 29, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Falconer distance set problem using Fourier analysis - Hong Wang
Analysis Seminar Topic: Falconer distance set problem using Fourier analysis Speaker: Hong Wang Affiliation: Member, School of Mathematics Date: November 2, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
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
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
Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
Viviani's Theorem: "Proof" Without Words
Link: https://www.geogebra.org/m/BXUrfwxj
From playlist Geometry: Challenge Problems
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
Hausdorff Dimension Analogues of the Elekes - Ronyai Theorem and Related Problems - Orit Raz
Computer Science/Discrete Mathematics Seminar II Topic: Hausdorff Dimension Analogues of the Elekes - Ronyai Theorem and Related Problems Speaker: Orit Raz Affiliation: Hebrew University; Visitor, School of Mathematics Date: April 04, 2023 If f is a real polynomial and A and B are finit
From playlist Mathematics
Proof: The Angle Bisector Theorem
This video states and proves the angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Relationships with Triangles
Peter Scholze - 2/3 The Langlands Program and the Moduli of Bundles on the Curve
I will speak about my joint work about the geometrization of the local Langlands correspondence. Peter Scholze (Univ. Bonn) Laurent Fargues (IMJ-PRG)
From playlist 2022 Summer School on the Langlands program
Scattering amplitudes (Lecture 3) by Freddy Cachazo
Statistical Physics Methods in Machine Learning DATE:26 December 2017 to 30 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "th
From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018
Hodge theory, coniveau and algebraic cycles - Claire Voisin
Claire Voisin Centre national de la recherche scientifique; Distinguished Visiting Professor, School of Mathematics October 6, 2014 My talk will be a broad introduction to what is the (mostly conjectural) higher dimensional generalization of Abel's theorem on divisors on Riemann surfaces,
From playlist Mathematics
Title: Differential Fields—A Model Theorist's View May 2016 Kolchin Seminar Workshop
From playlist May 2016 Kolchin Seminar Workshop
This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude. #math #geometry #mtbos #manim #animation #theorem #pww #proofwith
From playlist MathShorts
Incidence Theory and Uniform Distribution in Higher Dimensions - Alex Iosevich
Special Year Research Seminar Topic: Incidence Theory and Uniform Distribution in Higher Dimensions Speaker: Alex Iosevich Affiliation: University of Rochester Date: February 14, 2023 2:00pm Simonyi Hall 101 Incidence bound for points and spheres in higher dimensions generally becomes tr
From playlist Mathematics
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part5)
We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersecti
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Huawei Young Talents Programme - Zhe Sun
The online ceremony celebrating the official launch of the Huawei Young Talents Program at the Institut des Hautes Etudes Scientifiques was held on 6 November 2020. This program aims to support the work of talented researchers in mathematics and theoretical physics at the beginning of thei
From playlist Huawei Young Talents Program - November 2020
In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The
From playlist Other Math Videos
Weekly Space Hangout – Feb.26, 2016: Fast Radio Bursts & Missing Baryons
Host: Fraser Cain (@fcain) Guests: Kimberly Cartier (@AstroKimCartier ) Dave Dickinson (www.astroguyz.com / @astroguyz) Jolene Creighton (fromquarkstoquasars.com / @futurism) Nicole Gugliucci (cosmoquest.org / @noisyastronomer) Their stories this week: Mysterious Fast Radio Bursts Solve
From playlist Weekly Space Hangout