Nov 14, 2014 @ Urania

Correspondence with Friday speaker

My abstract is below, it may be helpful.

A key word would be CAT(k) space or CAT(0) space.

These are Alexandrov spaces of curvature bounded above. The other kind of Alexandrov space has curvature bounded below, and that would be a key phrase. (Note that topologists use Alexandrov space to mean something different; I see wikiedia has a mistaken link because of this.)

Just let me know if you need something else.

Looking forward to the visit!




has a link to notes for a minicourse I taught recently in Switzerland and Italy. Some initial stuff might be useful, but certainly the notes contain too much info!


Title: Alexandrov Spaces

Abstract: Alexandrov spaces of curvature bounded either below or above grew out of intuitive geometric tools developed by Alexandrov in the 1940's to study surfaces in Eucllidean 3-space. The two subjects "below" and "above" developed independently into revolutionary theories.

In the 1980's, Gromov's compactness theorem turned attention toward singular spaces that occur as limits of smooth Riemannian manifolds. Under a uniform lower sectional curvature bound, such limits are Alexandrov spaces of curvature bounded below. An explosion of work followed. More recently, these spaces informed Perelman's solution of the Poincare conjecture.

Alexandrov spaces of curvature bounded above play a role in Gromov's theory of hyperbolic groups. A beautiful recent application of these spaces was an estimate on billiard collisions that solved a famous problem in mechanics.

In her talk, Alexander will introduce the basics of Alexandrov geometry through examples, and present some personal favorite themes, applications and possible future directions. 

Correspondence with "What is ...?" speaker

Dear Mimi,

I will be happy to give a short introduction to CAT(0) geometry.

Best, Sebastian

Von: Holger Reich

Gesendet: 03.11.2014 15:41


Betreff: Fwd: What is ... a CAT(0) space?

Dear all,

is there among us a volunteer for a What is ...? talk on the BMS friday November 11th. Topic: What is a CAT(kappa)-space? See below.

Best, Holger


Topic revision: r3 - 18 Nov 2014, LutzPrechelt
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