Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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)
EXTRA MATH Lec 6B: Maximum likelihood estimation for the binomial model
Forelæsning med Per B. Brockhoff. Kapitler:
From playlist DTU: Introduction to Statistics | CosmoLearning.org
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
On the Fourier coefficients of a Cohen-Eisenstein series by Srilakshmi Krishnamoorthy
12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution.
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
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
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
Wave-front set of some representations... of the group SO(2n+1) - Jean-Loup Waldspurger
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Wave-front set of some representations of unipotent reduction of the group SO(2n+1) Speaker: Jean-Loup Waldspurger Affiliation: Univeristy of Jussieu Date: March 5, 2018 For more videos, please visit http:/
From playlist Mathematics
Irène Waldspurger: "Rank optimality of the Burer-Monteiro factorization"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop II: PDE and Inverse Problem Methods in Machine Learning "Rank optimality of the Burer-Monteiro factorization" Irène Waldspurger - Université Paris Dauphine Abstract: The Burer-Monteiro factorization is a classical heuristic used to spee
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Rank optimality for the Burer-Monteiro factorization - Waldspurger - Workshop 3 - CEB T1 2019
Irène Waldspurger (CNRS and Paris-Dauphine) / 03.04.2019 Rank optimality for the Burer-Monteiro factorization In the last decades, semidefinite programs have emerged as a a powerful way to solve difficult combinatorial optimization problems in polynomial time. Unfortunately, they are di
From playlist 2019 - T1 - The Mathematics of Imaging
Introduction to additive combinatorics lecture 9.5 --- Freiman's theorem for subsets of F_p^N.
Freiman's theorem for subsets of F_p^N states that if A is a subset of F_p^N and |A + A| is at most C|A|, then there is a subspace X of F_p^N of size at most C'|A| that contains A, where C' depends only on C. The result is actually due to Imre Ruzsa. Here I give not Ruzsa's original proof,
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Shou-Wu Zhang: Congruent number problem and BSD conjecture
Abstract : A thousand years old problem is to determine when a square free integer n is a congruent number ,i,e, the areas of right angled triangles with sides of rational lengths. This problem has a some beautiful connection with the BSD conjecture for elliptic curves En:ny2=x3−x. In fact
From playlist Jean-Morlet Chair - Research Talks - Prasad/Heiermann
Applying reimann sum for the midpoint rule and 3 partitions
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
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
Standard and Nonstandard Comparisons of Relative Trace Formulas - Yiannis Sakellaridis
Yiannis Sakellaridis Rutgers, The State University of New Jersey March 1, 2013 The trace formula has been the most powerful and mainstream tool in automorphic forms for proving instances of Langlands functoriality, including character relations. Its generalization, the relative trace formu
From playlist Mathematics
Math Park - 03/02/2018 - Irène WALDSPURGER - MINIMISATION DE FONCTIONS CONVEXES
Dans cet exposé, nous nous intéresserons à un problème apparemment basique : comment trouver la valeur minimale d'une fonction à valeurs réelles (si elle existe, bien entendu) ? Lorsqu'il est impossible de donner une formule exacte pour cette valeur, on doit avoir recours à des méthodes ap
From playlist Séminaire Mathematic Park
Raphaël Beuzart-Plessis: The local Gan-Gross-Prasad conjecture for unitary groups
Abstract: The local Gan-Gross-Prasad conjectures concern certain branching or restriction problems between representations of real or p-adic Lie groups. In its simplest form it predicts certain multiplicity-one results for "extended" L-packets. In a recent series of papers, Waldspurger has
From playlist Jean-Morlet Chair - Prasad/Heiermann
Introduction to additive combinatorics lecture 11.2 --- Part of the proof of Roth's theorem
Roth's theorem, one of the fundamental results of additive combinatorics, states that for every positive δ and every positive integer k there exists a positive integer n such that every subset of {1,2,...,n} of size at least δn contains an arithmetic progression of length 3. (This was late
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Periods, cycles, and L-functions: A relative trace formula approach – Wei Zhang – ICM2018
Number Theory Invited Lecture 3.10 Periods, cycles, and L-functions: A relative trace formula approach Wei Zhang Abstract: Motivated by the formulas of Gross–Zagier and Waldspurger, we review conjectures and theorems on automorphic period integrals, special cycles on Shimura varieties, a
From playlist Number Theory