In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a domain which is maximal in the sense that there exists a holomorphic function on this domain which cannot be extended to a bigger domain. Formally, an open set in the n-dimensional complex space is called a domain of holomorphy if there do not exist non-empty open sets and where is connected, and such that for every holomorphic function on there exists a holomorphic function on with on In the case, every open set is a domain of holomorphy: we can define a holomorphic function with zeros accumulating everywhere on the boundary of the domain, which must then be a natural boundary for a domain of definition of its reciprocal. For this is no longer true, as it follows from Hartogs' lemma. (Wikipedia).
Phylum Xenacoelomorpha and an Introduction to Nephrozoa
Most of the animals we are familiar with are contained in Nephrozoa, as these are the triploblastic and bilaterally symmetrical animals. The phyla we've covered so far are not part of Nephrozoa, and we have one more to cover before we get there, Xenocoelomorpha. This contains worm-like tri
From playlist Zoology
What are domains of holomorphy?
We define domains of holomorphy in C^n. We introduce holomorphically convex domains. We state the Cartan-Thullen theorem, and list consequences. One if them provides the existence of a smallest domain of holomorphy containing a fixed domain. For more details see Hormander's "An introducti
From playlist Several Complex Variables
Domains of holomorphy and Dolbeault cohomology
Domains of holomorphy can be characterized by vanishing of Dolbeault cohomology. We prove one direction of this characterization. For more detais see Gunning's "Introduction to holomorphic functions of several variables, Vol 1", Section G. Please point out any imprecisions in the comments
From playlist Several Complex Variables
Holomorphic tensors, fundamental groups and universal...(Lecture - 04) by Frederic Campana
20 March 2017 to 25 March 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions between mathematics and theoretical physics, especially
From playlist Complex Geometry
In this lecture I prove the Cartan-Thullen theorem. For more information see my previous video on the channel.
From playlist Several Complex Variables
Deforming Holomorphic Chern-Simons at Large N - Si Li
More videos on http://video.ias.edu
From playlist Natural Sciences
Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 3)
Non singular holomorphic foliations on Stein manifolds (Part 3)
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
H. Reis - Introduction to holomorphic foliations (Part 4)
The purpose of this course is to present the basics of the general theory of (singular) holomorphic foliations. We will begin with the general definition of a (regular) foliation and its relation with Frobenius Theorem. We will then introduce the singular analogues of these notions in the
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
Disk counting via family Floer theory - Hang Yuan
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Disk counting via family Floer theory Speaker: Hang Yuan Affiliation: Stony Brook University Date: May 28, 2021 Given a family of Lagrangian tori with full quantum corrections, the non-archimedean SYZ mirror construc
From playlist Mathematics
H. Reis - Introduction to holomorphic foliations (Part 1)
The purpose of this course is to present the basics of the general theory of (singular) holomorphic foliations. We will begin with the general definition of a (regular) foliation and its relation with Frobenius Theorem. We will then introduce the singular analogues of these notions in the
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
Samuel Grushevsky: Limits of zeroes of holomorphic differential on stable nodal Riemann surfaces
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Dynamical Systems and Ordinary Differential Equations
L^2 geometry of moduli spaces of vortices and lumps (Lecture 1) by James Martin Speight
PROGRAM VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual field the
From playlist Vortex Moduli - 2023
Phylum Rotifera Part 1: General Characteristics
It's time to wrap up our study of Gnathifera, and this means investigating phylum Rotifera. These are the wheel animals, and we will need a few tutorials to get through them all. Some species are free-living and some are parasitic, and you've probably had some in your body, since they're p
From playlist Zoology
Research Methods of Biopsychology
With some information regarding the organization of neurons and neural pathways, we are ready to start getting into some deeper topics. But before we do that, it will be useful to get a general sense of precisely how we learn about the things we will be discussing. The brain is complicated
From playlist Biopsychology
Positivity and algebraic integrability of holomorphic foliations – Carolina Araujo – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.7 Positivity and algebraic integrability of holomorphic foliations Carolina Araujo Abstract: The theory of holomorphic foliations has its origins in the study of differential equations on the complex plane, and has turned into a powerful t
From playlist Algebraic & Complex Geometry
Henri Epstein - Archeological Remarks on Analyticity Properties in Momentum Space in QFT
I will describe the foundations of the program of studying the analyticity properties of the n-point functions in momentum space : the primitive domain of analyticity and methods to enlarge it. If time permits, some of the results for the 4-point function will be described. Henri Epstein
From playlist Les séminaires de l'IHES
Analytic continuation in higher dimensions
In this short lecture I will prove the Hartogs theorem stating that holomorphic functions can be continued across compacts subsets if the dimension is at least 2. The proof will use solution of the del bar problem with compact support. For more details see Section 2.3 in Hormander's "Intro
From playlist Several Complex Variables
IGA - Lars Sektnan Extremal Kähler metrics on blowups
Abstract: Extremal Kähler metrics were introduced by Calabi in the 80’s as a type of canonical Kähler metric on a Kähler manifold, and are a generalisation of constant scalar curvature Kähler metrics in the case when the manifold admits automorphisms. A natural question is when the blowup
From playlist Informal Geometric Analysis Seminar
H. Reis - Introduction to holomorphic foliations (Part 3)
The purpose of this course is to present the basics of the general theory of (singular) holomorphic foliations. We will begin with the general definition of a (regular) foliation and its relation with Frobenius Theorem. We will then introduce the singular analogues of these notions in the
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
N=2* SU(2) Supersymmetric Yang-Mills Theory and Four-Manifold Invariants - Gregory Moore
High Energy Theory Seminar N=2* SU(2) Supersymmetric Yang-Mills Theory and Four-Manifold Invariants Speaker: Gregory Moore Affiliation: Rutgers University Date: March 15, 2021 For more video please visit http://video.ias.edu
From playlist IAS High Energy Theory Seminar