Universität Wien

250136 VO Alexandrov spaces (2018S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Oral Examination with one of the lecturers on individual appointment.

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

Literatur

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)

Zuordnung im Vorlesungsverzeichnis

MGEV

Letzte Änderung: Di 19.09.2023 00:22