Theorems in complex analysis | Conjectures that have been proved | Conjectures

De Branges's theorem

In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was posed by Ludwig Bieberbach and finally proven by Louis de Branges. The statement concerns the Taylor coefficients of a univalent function, i.e. a one-to-one holomorphic function that maps the unit disk into the complex plane, normalized as is always possible so that and . That is, we consider a function defined on the open unit disk which is holomorphic and injective (univalent) with Taylor series of the form Such functions are called schlicht. The theorem then states that The Koebe function (see below) is a function in which for all , and it is schlicht, so we cannot find a stricter limit on the absolute value of the th coefficient. (Wikipedia).

Video thumbnail

Proof of Lemma and Lagrange's Theorem

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div

From playlist Abstract Algebra

Video thumbnail

E. Fricain - Systèmes représentant dans les espaces de Hilbert de fonctions analytiques

Dans les espaces de Banach de dimension infinie, la notion de base de Schauder est classique et bien étudi ée. Elle permet de représenter tout élément de l’espace comme une série des éléments de la base de Schauder. Si on omet l’unicité des coefficients dans

From playlist Rencontres du GDR AFHP 2019

Video thumbnail

Quantum fluids of light in semiconductor microcavities by Jacqueline Bloch

Open Quantum Systems DATE: 17 July 2017 to 04 August 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore There have been major recent breakthroughs, both experimental and theoretical, in the field of Open Quantum Systems. The aim of this program is to bring together leaders in the Open Q

From playlist Open Quantum Systems

Video thumbnail

Abstract Algebra | Lagrange's Theorem

We prove some general results, culminating in a proof of Lagrange's Theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

Video thumbnail

Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

Video thumbnail

Number Theory | Linear Diophantine Equations

We explore the solvability of the linear Diophantine equation ax+by=c

From playlist Divisibility and the Euclidean Algorithm

Video thumbnail

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)

Video thumbnail

How to Determine if Functions are Linearly Independent or Dependent using the Definition

How to Determine if Functions are Linearly Independent or Dependent using the Definition If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Th

From playlist Zill DE 4.1 Preliminary Theory - Linear Equations

Video thumbnail

FRONTLINE VIETNAM: The Operational Soldier

Activities in the jungles during the year of 1966.

From playlist FRONTLINE VIETNAM 1-30

Video thumbnail

Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

Video thumbnail

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

Video thumbnail

algebraic geometry 16 Desargues's theorem

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers Desargues's theorem and duality of projective space.

From playlist Algebraic geometry I: Varieties

Video thumbnail

Journée de la Revue d’histoire des mathématiques - Nicolas Michel - 01/12/17

Journée de la Revue d’histoire des mathématiques (séance préparée par la rédaction de la RHM) Nicolas Michel (UMR SPHère, CNRS & Université Paris Diderot), « "Une proposition tantôt vraie, tantôt fausse" : autour de la controverse Chasles-De Jonquières » -----------------------------

From playlist Séminaire d'Histoire des Mathématiques

Video thumbnail

Interview au Cirm : Claire Voisin

Interview de Claire Voisin réalisée au Cirm. Avril 2018 Claire Voisin, mathématicienne française, est Directrice de recherche au Centre national de la recherche scientifique (CNRS) à l'Institut de mathématiques de Jussieu, elle est membre de l'Académie des sciences et titulaire de la nouv

From playlist Algebraic and Complex Geometry

Video thumbnail

A new basis theorem for ∑13 sets

Distinguished Visitor Lecture Series A new basis theorem for ∑13 sets W. Hugh Woodin Harvard University, USA and University of California, Berkeley, USA

From playlist Distinguished Visitors Lecture Series

Video thumbnail

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 6) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

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

Video thumbnail

Rellich Kondrachov Theorem for L^2 curvatures in arbitrary dimension- Tristan Rivière

Workshop on Geometric Functionals: Analysis and Applications Topic: Rellich Kondrachov Theorem for L^2 curvatures in arbitrary dimension Speaker: Tristan Rivière Affiliation: ETH Zürich; Member, School of Mathematics Date: March 5, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Related pages

Absolute value | Complex analysis | Askey–Gasper inequality | Lebedev–Milin inequality | Fekete–Szegő inequality | Entire function | De Branges space | Univalent function | Grunsky matrix | Nevanlinna's criterion | Complex plane | Schwarz lemma | Affine transformation | Schramm–Loewner evolution | Charles Loewner | Riemann mapping theorem | Richard Askey | Taylor series | Holomorphic function | Hilbert space