Two-dimensional objects--the torus and genus | Algebraic Topology 5 | NJ Wildberger
This is the 5th lecture of this beginners course in Algebraic Topology. We introduce some other surfaces: the cylinder, the torus or doughnut, and the n-holed torus. We define the genus of a surface in terms of maximal number of disjoint curves that do not disconnect it. We discuss how the
From playlist Algebraic Topology
Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th
From playlist Algebraic Topology
AlgTop5: Two-dimensional objects- the torus and genus
We introduce some surfaces: the cylinder, the torus or doughnut, and the n-holed torus. We define the genus of a surface in terms of maximal number of disjoint curves that do not disconnect it. We discuss how the plane covers the cylinder and the torus, and the associated group of translat
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Algebraic Expressions (Basics)
This video is about Algebraic Expressions
From playlist Algebraic Expressions and Properties
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
Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with many rings,and transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2014,AkiraNishihara
From playlist 3D printed toys
BAG1.2. Toric Varieties 2 - Affine Toric Varieties
Basic Algebraic Geometry: We define affine toric varieties. There are four ways to characterize ATVs and we note three here: as the Zariski closure of a torus in C^s; as the space for a torus group action; and as the variety of a toric ideal.
From playlist Basic Algebraic Geometry
To a topologist, a coffee cup and a donut are the same thing.
From playlist Algebraic Topology
Applied topology 3: A punctured torus is homotopy equivalent to a figure eight
Applied topology 3: A punctured torus is homotopy equivalent to a figure eight Abstract: We give an impromptu explanation of why a punctured torus (i.e., a torus with a single point removed) is homotopy equivalent to a figure eight (i.e., two circles glued together at a single point). In
From playlist Applied Topology - Henry Adams - 2021
Nonlinear algebra, Lecture 7: "Toric Varieties", by Mateusz Michalek
This is the seventh lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Mirror symmetry and cluster algebras – Paul Hacking & Sean Keel – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.15 Mirror symmetry and cluster algebras Paul Hacking & Sean Keel Abstract: We explain our proof, joint with Mark Gross and Maxim Kontsevich, of conjectures of Fomin–Zelevinsky and Fock–Goncharov on canonical bases of cluster algebras. We i
From playlist Algebraic & Complex Geometry
Parahoric Subgroups and Supercuspidal Representations of p-Adic groups - Dick Gross
Dick Gross Harvard University December 9, 2010 This is a report on some joint work with Mark Reeder and Jiu-Kang Yu. I will review the theory of parahoric subgroups and consider the induced representation of a one-dimensional character of the pro-unipotent radical. A surprising fact is th
From playlist Mathematics
Dimers and Beauville Integrable systems by Terrence George
PROGRAM: COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
A Continuous Transformation of a Double Cover of the Complex Plane into a Torus
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Dominic Milioto Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, a
From playlist Wolfram Technology Conference 2017
Nonlinear algebra, Lecture 9: "Representation Theory", by Mateusz Michalek
This is the ninth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
algebraic geometry 22 Toric varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes toric varieties as examples of abstract varieties. For more about these see the book "Introduction to toric varieties" by Fulton.
From playlist Algebraic geometry I: Varieties
Dimers and Integrability - Richard Kenyon
Richard Kenyon Brown University March 29, 2013 This is joint work with A. B. Goncharov. To any convex integer polygon we associate a Poisson variety, which is essentially the moduli space of connections on line bundles on (certain) bipartite graphs on a torus. There is an underlying integr
From playlist Mathematics
Entropy, Algebraic Integers and Moduli of Surfaces - Curtis McMullen
Curtis McMullen Harvard University December 7, 2010 For more videos, visit http://video.ias.edu
From playlist Mathematics
Topology of toric origami manifolds - Ana Pires
Ana Pires Member, School of Mathematics September 29, 2014 More videos on http://video.ias.edu
From playlist Mathematics
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology