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)
A Fibonacci bounded partial sum of the Harmonic series.
We determine the limit of a certain sequence defined in terms of Fibonacci and Harmonic numbers. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Identities involving Fibonacci numbers
Markus Banagl : The L-Homology fundamental class for singular spaces and the stratified Novikov
Abstract : An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for
From playlist Topology
A Correspondence Between Obstructions and Constructions for Staircases in Hirzebruch - Nicole Magill
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar A Correspondence Between Obstructions and Constructions for Staircases in Hirzebruch Surfaces Speaker: Nicole Magill Affiliation: Cornell University Date: October 28, 2022 The ellipsoidal embedding function of a symp
From playlist Mathematics
Lars Martin Sektnan: Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces
Abstract: In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact Kähler manifolds, and stability of pairs, in the toric case. Using constructions of Legendre and Apostolov-Calderbank-Gauduchon, we completely c
From playlist Analysis and its Applications
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
Prove the Derivative of a Constant: d/dx[c]
This video proves the derivative of a constant equals zero. http://mathispower4u.com
From playlist Calculus Proofs
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
Matthew Stover: Variations on an example of Hirzebruch
Abstract: In '84, Hirzebruch constructed a very explicit noncompact ball quotient manifold in the process of constructing smooth projective surfaces with Chern slope arbitrarily close to 3. I will discuss how this and some closely related ball quotients are useful in answering a variety of
From playlist Algebraic and Complex Geometry
The Weil-Petersson current for moduli of vector bundles and... by Schumacher
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Math 139 Fourier Analysis Lecture 04: Uniqueness of Fourier Series
Uniqueness of Fourier Series: all Fourier coefficients vanish implies function vanishes at points of continuity; absolute convergence of Fourier series implies uniform convergence of Fourier series to the original (continuous) function; twice continuous differentiability implies absolute c
From playlist Course 8: Fourier Analysis
My joint work with Armand Borel from 1952-1954 - Frederich Hirzebruch
75th Anniversary Celebration School of Mathematics Frederich Hirzebruch Bonn University March 12, 2005 More videos on http://video.ias.edu
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
A Complete Dichotomy Rises from the Capture of Vanishing Signatures - Jin-Yi Cai
Jin-Yi Cai University of Wisconsin November 19, 2012 Holant Problems are a broad framework to describe counting problems. The framework generalizes counting Constraint Satisfaction Problems and partition functions of Graph Homomorphisms. We prove a complexity dichotomy theorem for Holant
From playlist Mathematics
This lecture is part of an online course on schemes, following the book "Algebraic geometry" by Hartshorne. In this lecture we discuss a relative version of the construction of a projective scheme from a graded algebra, special cases of which give projective space bundles and the blowup
From playlist Algebraic geometry II: Schemes
This lecture give an overview of Chern classes of nonsingular algebraic varieties. We first define the Chern class of a lline bundle by looking at the cycle of zeros of a section. Then we define Chern classes of higher rank vector bundles by looking at the line bundle O(1) over the corresp
From playlist Algebraic geometry: extra topics
Birational geometry of complex hyperbolic manifolds - Gabriele di Cerbo
Gabriele di Cerbo Columbia University November 19, 2014 In 1984 Hirzebruch constructed the first examples of smooth toroidal compactifications of ball quotients with non-nef canonical divisor. In this talk, I will show that if the dimension is greater or equal than three then such example
From playlist Mathematics
Proof - the Derivative of a Constant Times a Function: d/dx[cf(x)]
This video proves the derivative of a constant times a function equals the constant time the derivative of f(x). http://mathispower4u.com
From playlist Calculus Proofs
Fabrizio Catanese: New examples of rigid varieties and criteria for fibred surfaces [...]
Abstract: Given an algebraic variety defined by a set of equations, an upper bound for its dimension at one point is given by the dimension of the Zariski tangent space. The infinitesimal deformations of a variety X play a somehow similar role, they yield the Zariski tangent space at the
From playlist Algebraic and Complex Geometry