Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
Reducibility for the Quasi-Periodic Liner Schrodinger and Wave Equations - Lars Hakan Eliasson
Lars Hakan Eliasson University of Paris VI; Institute for Advanced Study February 21, 2012 We shall discuss reducibility of these equations on the torus with a small potential that depends quasi-periodically on time. Reducibility amounts to "reduce” the equation to a time-independent linea
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
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
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
Alina Ostafe: Dynamical irreducibility of polynomials modulo primes
Abstract: In this talk we look at polynomials having the property that all compositional iterates are irreducible, which we call dynamical irreducible. After surveying some previous results (mostly over finite fields), we will concentrate on the question of the dynamical irreducibility of
From playlist Number Theory Down Under 9
An Elementary Proof of the Restricted Invertibility Theorem - Nikhil Srivastava
Nikhil Srivastava Institute for Advanced Study November 9, 2010 We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subs
From playlist Mathematics
David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
In this video, we present a geometric proof of the Pythagorean theorem. This famous theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Our proof utilizes the prin
From playlist Shorts
The Duffin-Schaeffer Conjecture - James Maynard
Hermann Weyl Lectures Topic: The Duffin-Schaeffer Conjecture Speaker: James Maynard Affiliation: Member, School of Mathematics Date: November 09, 2022 Given any non-negative function \f:ℤ→ℝ, it follows from basic ergodic ideas that either 100% of real numbers α have infinitely many ratio
From playlist Hermann Weyl Lectures
Efficient Stability for the Weyl-Heisenberg Group - Thomas Vidick
Marston Morse Lectures Topic: Efficient Stability for the Weyl-Heisenberg Group Speaker: Thomas Vidick Affiliation: California Institute of Technology Date: March 31, 2023 The question of stability of approximate group homomorphisms was first formulated by Ulam in the 1940s. One of the m
From playlist Mathematics
Polynomial Progressions in Topological Fields and Their Applications to Pointwise... - Mariusz Mirek
Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory Topic: Polynomial Progressions in Topological Fields and Their Applications to Pointwise Convergence Problems Speaker: Mariusz Mirek Affiliation: Member, School of Mathematics Date: March 02, 2023 We will discuss mu
From playlist Mathematics
To learn to think like a scientist check out http://Brilliant.org/SpaceTime PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE Check out the new Space Time Merch Store! https://pbsspacetime.com/ Support Space Time on Patreo
From playlist Understanding the Holographic Universe
Marco Mackaay: Certain subquotients of affine A 2
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: I will first recall the correspondence between the simple transitive 2-represen- tations of Uq(sl2)-mod, for q an even root of unity, and those of dihedra
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Recent developments in Quantum Magnetism by Gang Chen
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
Unique and 2:2 Games, Grassmannians, and Expansion - Irit Dinur
Hermann Weyl Lectures Topic: Unique and 2:2 Games, Grassmannians, and Expansion Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor Affiliation: School of Mathematics Date: November 20, 2019 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
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
Simultaneous Small Fractional Parts of Polynomials - James Maynard
Hermann Weyl Lectures Topic: Simultaneous Small Fractional Parts of Polynomials Speaker: James Maynard Affiliation: Member, School of Mathematics Date: November 07, 2022 Given several real numbers α1,...,αk, how well can you simultaneously approximate all of them by rationals which each
From playlist Hermann Weyl Lectures
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