Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Index theory of singular structures
Semester
WiSe 2017 / 18

Lecturer
Karsten Bohlen

Type of course (Veranstaltungsart)
Vorlesung

Contents
The Atiyah-Singer index theorem is a fundamental discovery in the history of mathematics. The
theorem states that for any compact manifold without boundary the Fredholm index of elliptic
operators is expressed as a topological formula, depending only on the stable homotopy class of the
principal symbol of the given operator. This result has numerous deep applications, e.g. to the
geometry of Riemannian manifolds and the study of partial differential equations. However
mathematical models of physical phenomena are often based on more general structures than the
classical smooth manifolds. Using techniques from non-commutative geometry we will study
generalizations of the Atiyah-Singer index theory to non-compact manifolds and spaces which have a
singular structure. E.g. the orbit spaces of group actions. The index theory of such foliation type
structures is strongly connected to versions of the Baum-Connes conjecture.

Recommended previous knowledge
Differential Geometry

Time/Date
Mittwoch 14-16 Uhr

Location
M103

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Passing the examination below
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 minutes, Date: individual, re-exam: Date:
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Pruefungsleistung
  • Unbenotet:
    • Bestehen der o. g. Pruefungsleistung
Modules
BV, MV, MGAGeo

ECTS
3