Complex surfaces | Abelian varieties | Complex manifolds
In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the complex dimension of M. All such complex structures can be obtained as follows: take a lattice Λ in a vector space V isomorphic to Cn considered as real vector space; then the quotient group is a compact complex manifold. All complex tori, up to isomorphism, are obtained in this way. For n = 1 this is the classical period lattice construction of elliptic curves. For n > 1 Bernhard Riemann found necessary and sufficient conditions for a complex torus to be an algebraic variety; those that are varieties can be embedded into complex projective space, and are the abelian varieties. The actual projective embeddings are complicated (see equations defining abelian varieties) when n > 1, and are really coextensive with the theory of theta-functions of several complex variables (with fixed modulus). There is nothing as simple as the cubic curve description for n = 1. Computer algebra can handle cases for small n reasonably well. By Chow's theorem, no complex torus other than the abelian varieties can 'fit' into projective space. (Wikipedia).
The torus magic is constructed with many rings. It transforms flat,spherical,etc. Farther more you can turn it inside out.
From playlist Handmade geometric toys
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
Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara
From playlist 3D printed toys
necklace,two way,Torus by Villarceau circles,mobius ball
From playlist Handmade geometric toys
Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with 20 large rings(50mm diameter) and many small rings.It transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2015,AkiraNishihara
From playlist 3D printed toys
Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara
From playlist 3D printed toys
Multivariable Calculus | The volume of a torus.
We use a triple integral to calculate the volume of a torus. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus | Multiple Integrals
Buy at http://www.shapeways.com/shops/GeometricToy This object consists of two "Torus Magic".These torus objects are constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,Akira Nishihara
From playlist 3D printed toys
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
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
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
Omer Bobrowski: Random Simplicial Complexes, Lecture III
A simplicial complex is a collection of vertices, edges, triangles, tetrahedra and higher dimensional simplexes glued together. In other words, it is a higher-dimensional generalization of a graph. In recent years there has been a growing effort in developing the theory of random simplicia
From playlist Workshop: High dimensional spatial random systems
Jon Pakianathan (5/7/19): On a canonical construction of tessellated surfaces from finite groups
Title: On a canonical construction of tessellated surfaces from finite groups Abstract: In this talk we will discuss an elementary construction that associates to the non-commutative part of a finite group’s multiplication table, a finite collection of closed, connected, oriented surfaces
From playlist AATRN 2019
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
Lagrangians, symplectomorphisms and zeroes of moment maps - Yann Rollin
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Lagrangians, symplectomorphisms and zeroes of moment maps Speaker: Yann Rollin Affiliation: Nantes University Date: April 08, 2022 I will present two constructions of Kähler manifolds, endowed with Hamiltonia
From playlist Mathematics
Classification results for two-dimensional Lagrangian tori - Dimitroglou Rizell
Princeton/IAS Symplectic Geometry Seminar Topic: Classification results for two-dimensional Lagrangian tori Speaker: Georgios Dimitroglou-Rizell Date: Thursday, April 7 We present several classification results for Lagrangian tori, all proven using the splitting construction from symp
From playlist Mathematics
Complexes of tori and rational points on homogeneous (...) - Harari - Workshop 1 - CEB T2 2019
David Harari (Université Paris Sud) / 20.05.2019 Complexes of tori and rational points on homogeneous spaces over a function field We explain new arithmetic duality theorems for finite group schemes and 2-term complexes of tori defined over a global field of positive characteristic. We
From playlist 2019 - T2 - Reinventing rational points
Andrew Lobb: Quantum sln knot cohomology and the slice genus
Abstract: We will give an overview of the information about the smooth slice genus so far yielded by the quantum 𝔰𝔩n knot cohomologies. Recording during the thematic meeting "Knotted Embeddings in Dimensions 3 and 4" the February 15, 2017 at the Centre International de Rencontres Mathémat
From playlist Topology
ComplexMultiplication 1/3 - i/3
From playlist Complex Multiplication