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401-3650-75L 4 Credits MSC D-MATH

Hilbert Complexes

Lecturers & Examiners: Prof. Dr. Ralf Hiptmair
Number of participants limited to 12. Fully booked.
VVZ CR n/a

Last Updated: 2026-06-01 11:31:24

Abstract

Seminar involves presentations based on research papers on theory and applications of the concept of Hilbert complexes.

Objective

Participants of the seminar should acquire familiarity with the concept of Hilbert complexes and know how it can be used as a tool for mathematical modeling. They should also learn how to present a scientific topic orally in an lucid, engaging, and well-structured way.

Content

The concept of Hilbert complexes was formally introduced by Jürgen Brüning and Matthias Lesch, in their 1992 paper: "Hilbert complexes", Journal of Functional Analysis, Vol. 108, Issue 1, 1992, Pages 88–132. They lifted on an abstract level fundamental properties of the most important specimen, the De Rham complex of differential forms on smooth manifolds. A Hilbert complex is a sequence of Hilbert spaces plus (unbounded) operators mapping between two successive spaces. The compositions of two of these operators vanish. It turns out that Hilbert complexes capture the algebraic structure of many important continuum field models in physics and engineering, like Maxwell's equations for electrodynamics, Stokes equations for viscous fluid flow, and the equations of 3D linear elasticity.

Resources

Literature

See Link

General Information

Language
English
Levels
MSC
Frequency
Yearly recurring

Examination

Type
ungraded semester performance

Registration & Places

Max Places
12
Signup End
19.09.2025
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Hilbert Complexes
  • Mon 16:15-18:00 (HG E 21)
2 h weekly

Offered In

  • Mathematik Master
    • Seminare und Semesterarbeiten
      • Seminare (ZUR BEACHTUNG: Damit die Zuteilung der verfügbaren Seminarplätze sich nicht primär auf den Zeitpunkt des Einschreibens in die Warteliste stützen muss, haben fast alle Mathematik-Seminare ein spezielles Auswahlverfahren. Eine direkte Belegung in myStudies ist dann nicht möglich, alle kommen zuerst auf die Warteliste. Ausserdem gilt: Die Auswahl an Mathematik-Seminaren wird auf 1 Seminar pro Semester beschränkt. Beachten Sie auch die Lerneinheit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)