I define topological manifolds. Motivated by the prospect of calculus on topological manifolds, I introduce smooth manifolds. At the end I point out how one needs to change the definitions, to obtain C^1 or even complex manifolds. To learn more about manifolds, see Lee's "Introduction to
From playlist Differential geometry
What is a Manifold? Lesson 10: Tangent Space - Basis Vectors
What is a Manifold? Lesson 10: Tangent Space - Basis Vectors
From playlist What is a Manifold?
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Manifolds
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
What is a Manifold? Lesson 14: Quotient Spaces
I AM GOING TO REDO THIS VIDEO. I have made some annotations here and annotations are not visible on mobile devices. STAY TUNED. This is a long lesson about an important topological concept: quotient spaces.
From playlist What is a Manifold?
Kyle Broder -- Recent Developments Concerning the Schwarz Lemma
A lecture I gave at the Beijing International Center for Mathematical Research geometric analysis seminar. The title being Recent Developments Concerning the Schwarz Lemma with applications to the Wu--Yau Theorem. This contains some recent results concerning the Bochner technique for the G
From playlist Research Lectures
L^2 methods, projective embeddings and Kahler-Einstein metrics (Lecture 1)by Ved Datar
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
Dror Varolin - Minicourse - Lecture 1
Dror Varolin Variations of Holomorphic Hilbert spaces Traditional complex analysis focuses on a single space, like a domain in Euclidean space, or more generally a complex manifold, and studies holomorphic maps on that space, into some target space. The typical target space for a domain i
From playlist Maryland Analysis and Geometry Atelier
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture - 2) 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
Geometry of Vortices on Riemann Surfaces (Lecture 4) by Oscar García-Prada
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 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 fie
From playlist Vortex Moduli - 2023
What is a Manifold? Lesson 5: Compactness, Connectedness, and Topological Properties
The last lesson covering the topological prep-work required before we begin the discussion of manifolds. Topics covered: compactness, connectedness, and the relationship between homeomorphisms and topological properties.
From playlist What is a Manifold?
Karen Strung: Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
Talk by Karen Strung in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 12, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Determinantal varieties and asymptotic expansion of Bergman kernels by Harald Upmeier
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
Mathematical Research Lecture -- Kyle Broder -- Curvature and Moduli
A recent talk I gave concerning the link between the curvature of the total space of a family of compact complex manifolds and the moduli-theoretic behaviour of the fibres. Part of this research appears in my Ph.D. thesis, and will appear in an upcoming preprint. 💪🙏 Support the channel b
From playlist Research Lectures
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture - 3) 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
Higgs bundles, harmonic maps, and applications by Richard Wentworth
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
Manifolds 2.2 : Examples and the Smooth Manifold Chart Lemma
In this video, I introduce examples of smooth manifolds, such as spheres, graphs of smooth functions, real vectorspaces, linear map spaces, and the Grassmannian of real vectorspaces (G_k(V)). Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Play
From playlist Manifolds