Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 1)
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
- audio 1 audio 2 audio 3
Descriptif
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics.- The Andreev-Koebe-Thurston theorem on circle packing polyhedral metrics and Marden-Rodin’s proof- Thurston’s conjecture on the convergence of circle packings to the Riemann mapping and its solution by Rodin-Sullivan- Finite dimensional variational principles associated to polyhedral surfaces- A discrete conformal equivalence of polyhedral surfaces and its relationship to convex polyhedra in hyperbolic 3-space- A discrete uniformization theorem for compact polyhedral surfaces- Convergence of discrete conformality and some open problems
Thèmes
Notice
Dans la même collection
-
Robert Young - Quantitative rectifiability and differentiation in the Heisenberg groupYoungRobert Kehoe.
(joint work with Assaf Naor) The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is unusually difficult to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of
-
Vincent Beffara - Percolation of random nodal linesBeffaraVincent
Percolation of random nodal lines
-
Melanie Rupflin - Horizontal curves of metrics and applications to geometric flowsRupflinMelanie
On closed surfaces there are three basic ways to evolve a metric, by conformal change, by pull-back with diffeomorphisms and by horizontal curves, moving orthogonally to the first two types of
-
Jeff Viaclovsky - Deformation theory of scalar-flat Kahler ALE surfacesViaclovskyJeff
I will discuss a Kuranishi-type theorem for deformations of complex structure on ALE Kahler surfaces, which will be used to prove that for any scalar-flat Kahler ALE surface, all small deformations of
-
Robert Haslhofer - The moduli space of 2-convex embedded spheres
We investigate the topology of the space of smoothly embedded n-spheres in R^{n+1}, i.e. the quotient space M_n:=Emb(S^n,R^{n+1})/Diff(S^n). By Hatcher’s proof of the Smale conjecture, M_2 is
-
Burkhard Wilking - Manifolds with almost nonnegative curvature operatorWilkingBurkhard
We show that n-manifolds with a lower volume bound v and upper diameter bound D whose curvature operator is bounded below by $-\varepsilon(n,v,D)$ also admit metrics with nonnegative curvature
-
Jean-Marc Schlenker - Anti-de Sitter geometry and polyhedra inscribed in quadricsSchlenkerJean-Marc
Anti-de Sitter geometry is a Lorentzian analog of hyperbolic geometry. In the last 25 years a number of connections have emerged between 3-dimensional anti-de Sitter geometry and the geometry of
-
Stéphane Saboureau - Sweep-outs, width estimates and volumeSabourauStéphane
Sweep-out techniques in geometry and topology have recently received a great deal of attention, leading to major breakthroughs. In this talk, we will present several width estimates relying on min-max
-
Igor Belegradek - Smoothness of Minkowski sum and generic rotationsBelegradekIgor
I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them. Here "generic" is understood in the sense of Baire category. The main
-
Feng Luo - Discrete conformal geometry of polyhedral surfaces and its convergenceLuoFeng
Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces. In this talk, we prove that discrete uniformizaton maps converge to
-
Greg McShane - Volumes of hyperbolics manifolds and translation distances
Schlenker and Krasnov have established a remarkable Schlaffli-type formula for the (renormalized) volume of a quasi-Fuchsian manifold. Using this, some classical results in complex analysis and Gromov
-
David Gabai - Maximal cusps of low volumeGabaiDavid
With Robert Haraway, Robert Meyerhoff, Nathaniel Thurston and Andrew Yarmola. We address the following question. What are all the 1-cusped hyperbolic 3-manifolds whose maximal cusps have low volume?
Avec les mêmes intervenants
-
Feng Luo - Discrete conformal geometry of polyhedral surfaces and its convergenceLuoFeng
Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces. In this talk, we prove that discrete uniformizaton maps converge to
-
Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 5)LuoFeng
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston
-
Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 4)LuoFeng
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston
-
Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 3)LuoFeng
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston
-
Feng Luo - An introduction to discrete conformal geometry of polyhedral surfaces (Part 2)LuoFeng
The goal of the course is to introduce some of the recent developments on discrete conformal geometry of polyhedral surfaces. We plan to cover the following topics. - The Andreev-Koebe-Thurston
Sur le même thème
-
R. Berman - Canonical metrics, random point processes and tropicalizationBermanRobert
In this talk I will present a survey of the connections between canonical metrics and random point processes on a complex algebraic variety X. When the variety X has positive Kodaira dimension,
-
B. Berndtsson - The curvature of (higher) direct images
I will first discuss some earlier work on the curvature of direct images of adjoint line bundles under a smooth proper fibration, or more generally a surjective map and (maybe) some of its
-
Robert Young - Quantitative rectifiability and differentiation in the Heisenberg groupYoungRobert Kehoe.
(joint work with Assaf Naor) The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is unusually difficult to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of
-
Vincent Beffara - Percolation of random nodal linesBeffaraVincent
Percolation of random nodal lines
-
Melanie Rupflin - Horizontal curves of metrics and applications to geometric flowsRupflinMelanie
On closed surfaces there are three basic ways to evolve a metric, by conformal change, by pull-back with diffeomorphisms and by horizontal curves, moving orthogonally to the first two types of
-
Jeff Viaclovsky - Deformation theory of scalar-flat Kahler ALE surfacesViaclovskyJeff
I will discuss a Kuranishi-type theorem for deformations of complex structure on ALE Kahler surfaces, which will be used to prove that for any scalar-flat Kahler ALE surface, all small deformations of
-
Burkhard Wilking - Manifolds with almost nonnegative curvature operatorWilkingBurkhard
We show that n-manifolds with a lower volume bound v and upper diameter bound D whose curvature operator is bounded below by $-\varepsilon(n,v,D)$ also admit metrics with nonnegative curvature
-
Jean-Marc Schlenker - Anti-de Sitter geometry and polyhedra inscribed in quadricsSchlenkerJean-Marc
Anti-de Sitter geometry is a Lorentzian analog of hyperbolic geometry. In the last 25 years a number of connections have emerged between 3-dimensional anti-de Sitter geometry and the geometry of
-
Stéphane Saboureau - Sweep-outs, width estimates and volumeSabourauStéphane
Sweep-out techniques in geometry and topology have recently received a great deal of attention, leading to major breakthroughs. In this talk, we will present several width estimates relying on min-max
-
Feng Luo - Discrete conformal geometry of polyhedral surfaces and its convergenceLuoFeng
Our recent joint work with D. Gu established a discrete version of the uniformization theorem for compact polyhedral surfaces. In this talk, we prove that discrete uniformizaton maps converge to
-
Igor Belegradek - Smoothness of Minkowski sum and generic rotationsBelegradekIgor
I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them. Here "generic" is understood in the sense of Baire category. The main
-
Greg McShane - Volumes of hyperbolics manifolds and translation distances
Schlenker and Krasnov have established a remarkable Schlaffli-type formula for the (renormalized) volume of a quasi-Fuchsian manifold. Using this, some classical results in complex analysis and Gromov