MathematischeGesellschaft Obstruction problems for geometric structures of compact type. |  |
Speaker:Giorgio Trentinaglia
Organizer:Mathematisches Institut
Details:
What should we mean by a "geometric structure" in general? The modern paradigm is that, ideally, geometric structures correspond to Cartan groupoids - that is, Lie groupoids endowed with multiplicative connections - and that the latter ought to be regarded as capturing all of the relevant "geometric content" of the original structures. This viewpoint stems from Klein's Erlangen program - or better, its far-reaching generalization proposed by É. Cartan - through the work of many (Ehresmann, Haefliger, ...). Within this fairly comprehensive conceptual framework, which includes present-day "intransitive" geometries, we can make sense of some very general problems, such as the following: What are the obstructions to the existence of geometric structures? What are the obstructions to deforming two geometric structures into each other? What are the global symmetries of geometric structures?In a variety of examples, the Cartan groupoid associated with a geometric structure happens to be proper (or even compact); these are the geometric structures "of compact type" that we want to consider. It turns out that for these structures some general tools are available for the study of the problems that we have just mentioned.
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Type:Colloquium
Language:English
Category:Research
Host:Prof. Dr. Chenchang Zhu
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Direct link to event:https://events.goettingen-campus.de/event?eventId=11002
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