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Prof.Dr.habil. Ilka Agricola |  |
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Prof.Dr.habil. Ilka Agricola | |
Past Conferences:
Gemeinsames Mathematisches Kolloquium mit Gießen:
- SS 2011: Prof. Huisken am 15.6.2011
Activities in the Winter Term
2010/11:
Festkolloquium des Fachbereichs am 2.2.2011 [Fotos]
Activities in the Summer Term
2009:
- Öffentlicher Vortrag "Mathematik und Demokratie" von Prof. Dr. Friedrich Pukelsheim, Alte Aula, 18. Mai, 17 Uhr [Poster]
- Antrittsvorlesung "Dirac-operatoren und Geometrie", Alte Aula, 1. Juli, 18 Uhr. Bitte bei Frau Teubner anmelden!
Activities in the Summer Term
2008:
Concert "A Swing in the Park" by Consortium Musicum Bünde
- Music from five centuries by Gabrieli, Franck, Telemann and others
Saturday 28 June, 7 p.m., Ernst-Reuter-Saal (Reuter-Haus, Dorotheenstr. 24)
[map] [poster]
Activities in the Winter Term
2006/07:
Klausurtag 13. Oktober 2006:
Klausurtag der Arbeitsgruppe "Globale Analysis und Differentialgeometrie" ganztägig im Raum 1.410. Anschließend feierliche Verabschiedung von Pablo Ramacher.
Dr. S. Chiossi and Dr. R. Cleyton will organize a seminar on Deformation theory of complex structures.
Dr. habil. Ilka Agricola organisiert ein Seminar über Lie-Gruppen und homogene Räume.
Activities in the Winter Term
2004/05:
Prof. Dr. Andrew Swann (Odense) will give two 90-minutes lectures on
Quaternions and special holonomies.
Schedule: Monday, 24.01.2005 9:15-11:45 and Wednesday, 26.01.2005, 11:15-12:45 in the Seminar Room 1.315.
Abstract: The talks will circle around bundle constructions for metrics with reduced holonomy, like the Bryant-Salamon construction of G2 metrics and constructions of hypercomplex manifolds and twistor spaces based on the speaker's previous work.
Activities in the Winter Term
2003/04
Dr. Pawel Nurowski will give a series of 5 talks entitled
Introduction to Cartan's equivalence method.
Schedule: Tuesday 11.00-12.30 (!), room 4.005, Begin: 18.11.2003, end: 16.12.2003. See also the homepage of the Seminar "Special geometries and Holonomy".
Abstract: One of the problems in differential geometry is to determine as to whether two geometric structures defined on two manifolds are locally isomorphic. For example, given two Riemannian structures a question arises how to establish, in a finite number of steps, if there exists a local diffeomorphism that transforms one of the Riemanian structures into the other. This problem is particulary known in General Relativity, where a newly obtained exact solution of Einstein's field equations, usually expressed in some local coordinates, should be shown not to be transformable by a coordinate transformation to a solution already known.
The problem of determining if two geometric structures (G-structures, in modern language) are locally isomorphic is called `equivalence problem'. They were extensively studied by Elie Cartan (see Part 2 and Part 3 of Cartan's "Oeuvres Completes" , Gauthier-Villars, 1955) who developed a method, which in principle, enables one to solve equivalence problems for any given G-structure in a fairly algorithmic fashion. This method, called Cartan's equivalence method, will be discussed in these series of lectures.
Knowing the method one can use it to construct all the local invariants of the G-structure considered. For example Cartan used it to find the invariants of Riemannian, conformal, projective and CR structures. He also applied it to the structures that are associated with ODEs given modulo certain type of transformations of variables and to many others. Cartan's method may also be used to find all the G-structures with large symmetries and to determine the dimensions of the possible groups of symmetries of a given category of G-structures.
In the lectures we will discuss the following topics:
The lectures will be based on the textbook:
P. Olver "Equivalence, Invariants and Symmetry", Cambridge University Press, 1996, Ch. 8-13.
Other references of interest are: