Universität Wien
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250136 VO Alexandrov spaces (2018S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 05.03. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 06.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.03. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 20.03. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.04. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.04. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.04. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.04. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.04. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.04. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.04. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.05. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.05. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.05. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.05. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.06. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.06. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.06. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.06. 12:30 - 14:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.06. 13:15 - 14:45 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This is a course on metric geometry. The central idea of this field is to describe geometric properties (such as length, angles and curvature) in terms of metric distances alone. As it turns out, many notions familiar from differential geometry can indeed be captured in such "synthetic" terms alone.

The foundational notion is that of a length space, i.e., a metric space where the metric distance between two points is given by the infimum of the length of all connecting curves. Key examples are Riemannian manifolds and polyhedra.

Curvature bounds in such spaces are based on comparison with triangles in certain model spaces. E.g., the sphere has positive curvature because triangles are fatter than Euclidean triangles of the same sidelengths. Spaces with a curvature bound in this sense are called Alexandrov spaces.

Metric geometry, and in particular the theory of length spaces, is a vast and very active field of research that has found applications in diverse mathematical disciplines, such as differential geometry, group theory, dynamical systems and partial differential equations. It has led to
identifying the ‘metric core’ of many results in differential geometry, to clarifying the interdependence of various concepts, and to generalizations of central notions in the field to low regularity situations.

Assessment and permitted materials

Oral Examination with one of the lecturers on individual appointment.

Minimum requirements and assessment criteria

Examination topics

Reading list

Dmitri Burago, Yuri Burago, Sergei Ivanov, "A Course in Metric Geometry" (AMS, 2001)
Martin R. Bridson,‎ Andre Häfliger, "Metric Spaces of Non-Positive Curvature" (Springer, 2011)
Athanase Papadopoulos, "Metric Spaces, Convexity and Nonpositive Curvature" (EMS, 2004)

Association in the course directory

MGEV

Last modified: Tu 19.09.2023 00:22