Low-dimensional topology | Manifolds

A Guide to the Classification Theorem for Compact Surfaces is a textbook in topology, on the classification of two-dimensional surfaces. It was written by Jean Gallier and Dianna Xu, and published in 2013 by Springer-Verlag as volume 9 of their Geometry and Computing series (doi:10.1007/978-3-642-34364-3, ISBN 978-3-642-34363-6). The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. (Wikipedia).

Math 131 092116 Properties of Compact Sets

Properties of compact sets. Compact implies closed; closed subsets of compact sets are compact; collections of compact sets that satisfy the finite intersection property have a nonempty intersection; infinite subsets of compact sets must have a limit point; the infinite intersection of ne

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis

Math 101 Fall 2017 112917 Introduction to Compact Sets

Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi

From playlist Course 6: Introduction to Analysis (Fall 2017)

Math 101 Introduction to Analysis 112515: Introduction to Compact Sets

Introduction to Compact Sets: open covers; examples of finite and infinite open covers; definition of compactness; example of a non-compact set; compact implies closed; closed subset of compact set is compact; continuous image of a compact set is compact

From playlist Course 6: Introduction to Analysis

Complex surfaces 1: Introduction

This talk is part of a series giving an informal survey of complex algebraic surfaces. We give an overview of the Enriques-Kodaira classification, with examples of most of the different types of surfaces. We conclude by giving an example of a non-algebraic surface: the Hopf surface. Furth

From playlist Algebraic geometry: extra topics

algebraic geometry 23 Categories

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.

From playlist Algebraic geometry I: Varieties

Alexandre Sukhov - J-complex curves: some applications (Part 4)

We will focus in our lectures on the following : 1. J-complex discs in almost complex manifolds : general properties. Linearization and compactness. Gromov’s method : the Fredholm alternative for the d-bar operator. Attaching a complex disc to a Lagrangian manifold. Application : exotic sy

From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications

Growth of cohomology in towers of manifolds: a topological applica... - Mathilde Gerbelli-Gauthier

Members’ Colloquium Topic: Growth of cohomology in towers of manifolds: a topological application of the Langlands program Speaker: Mathilde Gerbelli-Gauthier Affiliation: Member, School of Mathematics Date: November 15, 2021 How does the dimension of the first cohomology grow in a tower

From playlist Mathematics

8ECM Invited Lecture: Burak Özbağcı

From playlist 8ECM Invited Lectures

Brent Pym: Holomorphic Poisson structures - lecture 3

The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a cano

From playlist Virtual Conference

The Computational Complexity of Geometric Topology Problems - Greg Kuperberg

Greg Kuperberg University of California, Davis September 24, 2012 This talk will be a partial survey of the first questions in the complexity theory of geometric topology problems. What is the complexity, or what are known complexity bounds, for distinguishing n-manifolds for various n? Fo

From playlist Mathematics

Complex surfaces 4: Ruled surfaces

This talk gives an informal survey of ruled surfaces and their role in the Enriques classification. We give a few examples of ruled surfaces, summarize the basic invariants of surfaces, and sketch how one classifies the surfaces of Kodaira dimension minus infinity.

From playlist Algebraic geometry: extra topics

Antoine Song - Spherical Plateau problem and applications

I will discuss an area minimization problem in certain quotients of the Hilbert sphere by countable groups. An early version of that setting appears in Besson-Courtois-Gallot’s work on the entropy inequality. As an application of this minimization problem, we obtain some stability results.

From playlist Not Only Scalar Curvature Seminar

J. Aramayona - MCG and infinite MCG (Part 3)

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the secon

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings

We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at infinity. The 3d flying wings are collapsed. For dimension n ≥ 4, we find a family of Z2 × O(n − 1

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Geometry of Surfaces - Topological Surfaces Lecture 4 : Oxford Mathematics 3rd Year Student Lecture

This is the fourth of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture covers connected sums, orientations, and finally the classificatio

From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces

Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology

24th Workshop in Geometric Topology, Calvin College, June 30, 2007

From playlist Ian Agol: 24th Workshop in Geometric Topology

Describing Functions (Discrete Math)

This video covered the various ways to describe functions in a discrete math class.

From playlist Functions (Discrete Math)

Dynamics on character varieties - William Goldman

Character Varieties, Dynamics and Arithmetic Topic: Dynamics on character varieties Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: November 10, 2021 In these two talks, I will describe how the classification of locally homogeneous geomet

From playlist Mathematics

Alexandre Sukhov - J-complex curves: some applications (Part 1)

We will focus in our lectures on the following : 1. J-complex discs in almost complex manifolds : general properties. Linearization and compactness. Gromov’s method : the Fredholm alternative for the d-bar operator. Attaching a complex disc to a Lagrangian manifold. Application : exotic sy

From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications