MATH331: Riemann Surfaces - part 1
We define what a Riemann Surface is. We show that PP^1 is a Riemann surface an then interpret our crazy looking conditions from a previous video about "holomorphicity at infinity" as coming from the definition of a Riemann Surface.
From playlist The Riemann Sphere
Curvature of a Riemannian Manifold | Riemannian Geometry
In this lecture, we define the exponential mapping, the Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature. The focus is on an intuitive explanation of the curvature tensors. The curvature tensor of a Riemannian metric is a very large stumbling block for many student
From playlist All Videos
Andreas Bernig: Intrinsic volumes on pseudo-Riemannian manifolds
The intrinsic volumes in Euclidean space can be defined via Steiner’s tube formula and were characterized by Hadwiger as the unique continuous, translation and rotation invariant valuations. By the Weyl principle, their extension to Riemannian manifolds behaves naturally under isometric em
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
[BOURBAKI 2019] Higher rank Teichmüller theories - Pozzetti - 30/03/19
Beatrice POZZETTI Higher rank Teichmüller theories Let Γ be the fundamental group of a compact surface S with negative Euler characteristic, and G denote PSL(2, R), the group of isometries of the hyperbolic plane. Goldman observed that the Teichmüller space, the parameter space of marked
From playlist BOURBAKI - 2019
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri (L1) by Sunil Mukhi
Seminar Lecture Series - Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri Speaker: Sunil Mukhi (IISER Pune) Date : Mon, 20 March 2023 to Fri, 21 April 2023 Venue: Online (Zoom & Youtube) ICTS is pleased to announce special lecture series by Prof. Sunil Mukh
From playlist Lecture Series- Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri -2023
Conformal Dynamics in Pseudo-Riemannian Geometry: a Question of A. Lichnerowicz - Charles Frances
Charles Frances Universite Paris-Sud 11; Member, School of Mathematics April 1, 2013 In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The
From playlist Mathematics
This talk is about some properties of plane curves used in the Riemann-Roch theorem. We first show that every nonsingular curve is isomorphic to a resolution of a plane curve with no singularities worse than ordinary double points (nodes). We then calculate the genus of plane curves with o
From playlist Algebraic geometry: extra topics
General Relativity Explained in 7 Levels of Difficulty
Go to https://nebula.tv/minutephysics to get access to Nebula (where you can watch the extended version of this video), plus you'll get a 20% discount on an annual subscription. This video covers the General theory of Relativity, developed by Albert Einstein, from basic simple levels (it'
From playlist MinutePhysics
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 2/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 1/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Convergence and Riemannian bounds on Lagrangian submanifolds - Jean-Philippe Chassé
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Title: Convergence and Riemannian bounds on Lagrangian submanifolds Speaker: Jean-Philippe Chassé Affiliation: UdeM Date: October 8, 2021 Abstract: Recent years have seen the appearance of a plethora of possible metrics on
From playlist PU/IAS Symplectic Geometry Seminar
Some identities involving the Riemann-Zeta function.
After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case - Nikhil Savale
Symplectic Dynamics/Geometry Seminar Topic: Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case Speaker: Nikhil Savale Affiliation: University of Cologne Date: October 28, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
A panoramic view of Mathematics Research @ICTS by Varun Thakre and Anish Mallick
ICTS In-house 2019 Organizers: Adhip Agarwala, Ganga Prasath, Rahul Kashyap, Gayathri Raman, Priyanka Maity Date and Time: 23rd April, 2019 Venue: Ramanujan Lecture Hall, ICTS Bangalore inhouse@icts.res.in An exclusive day to exchange ideas and discuss research amongst members of ICTS.
From playlist ICTS In-house 2019
Riemann Roch: structure of genus 1 curves
This talk is about the Riemann Roch theorem in the spacial case of genus 1 curves or Riemann surface. We show that a compact Riemann surface satisfying the Riemann Roch theorem for g=1 is isomorphic to a nonsingular plane cubic. We show that this is topologically a torus, and use this to s
From playlist Algebraic geometry: extra topics
Index Theory for Lorentzian Manifolds - Christian Bär
Seminar on Global Analysis Topic: Index Theory for Lorentzian Manifolds Speaker: Christian Bär Affiliation: University of Potsdam Date: November 15, 2022 Index theory goes back to Atiyah and Singer and deals with elliptic operators on Riemannian manifolds. It has numerous applications in
From playlist Mathematics
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming