Difference between revisions of "Geometry and Topology Seminar 2019-2020"
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The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang. | The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang. | ||
+ | |||
+ | === Jiyuan Han === | ||
+ | "TBA" | ||
=== Shaosai Huang === | === Shaosai Huang === |
Revision as of 11:28, 6 September 2017
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Alexandra Kjuchukova or Lu Wang .
Contents
Fall 2017
date | speaker | title | host(s) |
---|---|---|---|
September 8 | TBA | TBA | TBA |
September 15 | Jiyuan Han | TBA | Local |
September 22 | TBA | TBA | TBA |
September 29 | Ke Zhu(Minnesota State University) | "Isometric Embedding via Heat Kernel" | Bing Wang |
October 6 | Shaosai Huang(Stony Brook) | TBA | Bing Wang |
October 13 | (reserved) | TBA | Kjuchukova |
October 20 | Shengwen Wang (Johns Hopkins) | TBA | Lu Wang |
October 27 | Marco Mendez-Guaraco (Chicago) | TBA | Lu Wang |
November 3 | TBA | TBA | TBA |
November 10 | TBA | TBA | TBA |
November 17 | Ovidiu Munteanu (University of Connecticut) | TBA | Bing Wang |
Thanksgiving Recess | |||
December 1 | TBA | TBA | TBA |
December 8 | TBA | TBA | TBA |
Fall Abstracts
Marco Mendez-Guaraco
"TBA"
Ke Zhu
"Isometric Embedding via Heat Kernel"
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding. In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.
Jiyuan Han
"TBA"
Shaosai Huang
"TBA"
Ovidiu Munteanu
"TBA"
Shengwen Wang
"TBA"
Archive of past Geometry seminars
2016-2017 Geometry_and_Topology_Seminar_2016-2017
2015-2016: Geometry_and_Topology_Seminar_2015-2016
2014-2015: Geometry_and_Topology_Seminar_2014-2015
2013-2014: Geometry_and_Topology_Seminar_2013-2014
2012-2013: Geometry_and_Topology_Seminar_2012-2013
2011-2012: Geometry_and_Topology_Seminar_2011-2012
2010: Fall-2010-Geometry-Topology