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?
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 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?
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties
What is a Manifold? Lesson 18: Homotopy
What is a Manifold? Lesson 18: Introduction to Homotopy
From playlist What is a Manifold?
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties
What is a Manifold? Lesson 8: Diffeomorphisms
What is a Manifold? Lesson 8: Diffeomorphisms
From playlist What is a Manifold?
Alberto Cattaneo: An introduction to the BV-BFV Formalism
Abstract: The BV-BFV formalism unifies the BV formalism (which deals with the problem of fixing the gauge of field theories on closed manifolds) with the BFV formalism (which yields a cohomological resolution of the reduced phase space of a classical field theory). I will explain how this
From playlist Topology
Holomorphic Cartan geometries on simply connected manifolds by Sorin Dumitrescu
Discussion Meeting Complex Algebraic Geometry ORGANIZERS: Indranil Biswas, Mahan Mj and A. J. Parameswaran DATE:01 October 2018 to 06 October 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore The discussion meeting on Complex Algebraic Geometry will be centered around the "Infosys-ICT
From playlist Complex Algebraic Geometry 2018
Spectra in locally symmetric spaces by Alan Reid
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
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
A Tour of Skein Modules by Rhea Palak Bakshi
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Lecture 4: VOA[M4] (Lecture 3) by Sergei Gukov
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Noémie Combe - How many Frobenius manifolds are there?
In this talk an overview of my recent results is presented. In a joint work with Yu. Manin (2020) we discovered that an object central to information geometry: statistical manifolds (related to exponential families) have an F-manifold structure. This algebraic structure is a more general v
From playlist Research Spotlight
Hsueh-Yung Lin: On the existence of algebraic approximations of compact Kähler manifolds
Abstract: Let X be a compact Kähler manifold. The so-called Kodaira problem asks whether X has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Vo
From playlist Analysis and its Applications
Mohamed Boucetta: On the geometry of noncommutative deformations
Recording during the meeting "Workshop on Differential Geometry and Nonassociative Algebras" the November 12, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Geometry
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?
The Math You Didn't Learn | #SoME2
Sometimes people wonder what actual mathematicians do. Do they crunch large numbers? Participate in competitions with each other? (They actually did a lot of that in the Middle Ages). Are they geniuses whose activites are unfathomable for us normal people? Math is a very large field, but m
From playlist Summer of Math Exposition 2 videos