In the theory of functions of several complex variables, a branch of mathematics, a polydisc is a Cartesian product of discs. More specifically, if we denote by the open disc of center z and radius r in the complex plane, then an open polydisc is a set of the form It can be equivalently written as One should not confuse the polydisc with the open ball in Cn, which is defined as Here, the norm is the Euclidean distance in Cn. When , open balls and open polydiscs are not biholomorphically equivalent, that is, there is no biholomorphic mapping between the two. This was proven by Poincaré in 1907 by showing that their automorphism groups have different dimensions as Lie groups. When the term bidisc is sometimes used. A polydisc is an example of logarithmically convex Reinhardt domain. (Wikipedia).
The Bergman kernel of the polydisk and the ball
I compute the Bergman kernel of the unit polydisk and the unit Euclidean ball. For my previous video on the Bergman kernel see https://www.youtube.com/watch?v=loIC28LNgNM
From playlist Several Complex Variables
Contact non-squeezing via selective symplectic homology - Igor Uljarević
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Contact non-squeezing via selective symplectic homology Speaker: Igor Uljarević Affiliation: University of Belgrade Date: October 14, 2022 I will introduce a new version of symplectic homology that resembles
From playlist Mathematics
Symplectic convexity? (an ongoing story...)
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Symplectic convexity? (an ongoing story...) Speaker: Jean Gutt Affiliation: University of Toulouse Date: October 21, 2022 What is the symplectic analogue of being convex? We shall present different ideas to
From playlist Mathematics
Polymorphs can be a headache for people who make pharmaceuticals. Find out why? More chemistry at http://www.periodicvideos.com/
From playlist Chem Definition - Periodic Videos
In this lecture I prove the Cartan-Thullen theorem. For more information see my previous video on the channel.
From playlist Several Complex Variables
Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of ... (Part 2)
We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyp
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Nigel Higson: The Oka principle and Novodvorskii’s theorem
Talk by Jonathan Rosenberg in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on November 11, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
The 3-point spectral Pick interpolation problem by Vikramjeet Singh Chandel
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
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
What is a polygon and what is a non example of a one
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the definition of a regular polygon and how do you find the interior angles
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Classifying a polygon in two different ways ex 4
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are the names of different types of polygons based on the number of sides
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
On symplectic capacities and their blind spots - Ely Kerman
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: On symplectic capacities and their blind spots Speaker: Ely Kerman Affiliation: University of Illinois, Urbana-Champaign Date: February 11, 2022 In this talk I will discuss a joint project with Yuanpu Liang
From playlist Mathematics
What is the difference between convex and concave
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar 5/27/22
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Three 20-minute research talks Speaker: Daniel Rudolf (Ruhr-Universität Bochum): Viterbo‘s conjecture for Lagrangian products in ℝ4 We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian pro
From playlist Mathematics
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons