Structures on manifolds | Manifolds
In mathematics, an analytic manifold, also known as a manifold, is a differentiable manifold with analytic transition maps. The term usually refers to real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds such that singularities are permitted. For , the space of analytic functions, , consists of infinitely differentiable functions , such that the Taylor series converges to in a neighborhood of , for all . The requirement that the transition maps be analytic is significantly more restrictive than that they be infinitely differentiable; the analytic manifolds are a proper subset of the smooth, i.e. , manifolds. There are many similarities between the theory of analytic and smooth manifolds, but a critical difference is that analytic manifolds do not admit analytic partitions of unity, whereas smooth partitions of unity are an essential tool in the study of smooth manifolds. A fuller description of the definitions and general theory can be found at differentiable manifolds, for the real case, and at complex manifolds, for the complex case. (Wikipedia).
Math 135 Complex Analysis Lecture 07 021015: Analytic Functions
Definition of conformal mappings; analytic implies conformal; Cauchy-Riemann equations are satisfied by analytic functions; partial converses (some proven, some only stated); definition of harmonic functions; harmonic conjugates
From playlist Course 8: Complex Analysis
Holomorphic Curves in Compact Complex Parallelizable Manifold Γ\SL(2, C) by Ryoichi Kobayashi
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Analytic Geometry Over F_1 - Vladimir Berkovich
Vladimir Berkovich Weizmann Institute of Science March 10, 2011 I'll talk on work in progress on algebraic and analytic geometry over the field of one element F_1. This work originates in non-Archimedean analytic geometry as a result of a search for appropriate framework for so called skel
From playlist Mathematics
Equivariant principal bundles on toric varieties- Part 1 by Mainak Poddar
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Seshadri constants on projective varieties by Krishna Hanumanthu
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
In search of Lagrangians with non-trivial Floer cohomology by Sushmita Venugopalan
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Counting planar (genus 0) degree d curves in P^3 by Ritwik Mukherjee
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Homogeneous holomorphic foliations on Kobayashi hyperbolic manifolds by Benjamin Mckay
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Morse-Bott theory on singular analytic spaces and applications to the topology of… - Paul Feehan
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Morse-Bott theory on singular analytic spaces and applications to the topology of symplectic four-manifolds Speaker: Paul Feehan Affiliation: Rutgers University Date: November 29, 2021 We describe two extensions, called th
From playlist Mathematics
Pierre Albin : Extending the Cheeger-Müller theorem through degeneration
Abstract : Reidemeister torsion was the first topological invariant that could distinguish between spaces which were homotopy equivalent but not homeomorphic. The Cheeger-Müller theorem established that the Reidemeister torsion of a closed manifold can be computed analytically. I will repo
From playlist Topology
2022 10 Dan Coman: Extension of quasiplurisubharmonic functions
CONFERENCE Recording during the thematic meeting : "Complex Geometry, Dynamical Sytems and Foliation Theory" the October 20, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathemat
From playlist Analysis and its Applications
Rahim Moosa: Nonstandard compact complex manifolds with a generic auto-morphism
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 Logic and Foundations
Holomorphic rigid geometric structures on compact manifolds by Sorin Dumitrescu
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
L. Meersseman - Kuranishi and Teichmüller
Abstract - Let X be a compact complex manifold. The Kuranishi space of X is an analytic space which encodes every small deformation of X. The Teichmüller space is a topological space formed by the classes of compact complex manifolds diffeomorphic to X up to biholomorphisms smoothly isotop
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
On the geometry and topology of zero sets of Schrödinger eigenfunctions - Yaiza Canzani
Yaiza Canzani Member, School of Mathematics March 30, 2015 In this talk I will present some new results on the structure of the zero sets of Schrödinger eigenfunctions on compact Riemannian manifolds. I will first explain how wiggly the zero sets can be by studying the number of intersect
From playlist Mathematics
Pierre Albin: The sub-Riemannian limit of a contact manifold
Talk by Pierre Albin in the Global Noncommutative Geometry Seminar (Americas) on January 29, 2021. https://globalncgseminar.org/talks/tba-5/?utm_source=mailpoet&utm_medium=email&utm_campaign=global-noncommutative-geometry-seminar-americas-01292021_14
From playlist Global Noncommutative Geometry Seminar (Americas)
The Inner Equation for Generalized Standard Maps - Pau Martin
Pau Martin Universitat Poliecnica de Catalunya, Barcelona, Spain February 15, 2012 We study particular solutions of the "inner equation" associated to the splitting of separatrices on "generalized standard maps". An exponentially small complete expression for their difference is obtained.
From playlist Mathematics
Winding for Wave Maps - Max Engelstein
Analysis Seminar Topic: Winding for Wave Maps Speaker: Max Engelstein Affiliation: University of Minnesota Date: June 1, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Equivariant principal bundles on toric varieties- Part 2 by Arijit Dey
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018