KolloquiumGRK Lorentzian geometry, dominant energy condition and Dirac-Witten operators |  |
Speaker:Jonathan Glöckle, Universität Regensburg
Location:Mathematisches Institut, Bunsenstr 3-5Onlinehttps://uni-goettingen.zoom.us/j/91336854872Gras Geo Map
Organizer:Fakultät für Mathematik und Informatik
Details:
The development of Relativity Theory triggered the study of Lorentzian manifolds. Notions such as Levi-Civita connection or curvature easily generalize to these strange geometric objects, where certain directions are distinguished as “lightlike”. The Riemannian world of our experience enters again, when we are considering embedded spacelike hypersurfaces.
These do not only come with a Riemannian metric $g$ but also a second fundamental form $K$, describing the first order change of the metric. For physical reasons the pairs $(g, K)$ arising on such hypersurfaces are expected to satisfy a certain inequality -- the dominant energy condition -- that generalizes the condition of non-negative scalar curvature if $K = 0$. As for non-negative (or
positive) scalar curvature, index theoretic methods can be used to study the (strict) dominant energy condition. In this context Dirac-Witten operators serve as the appropriate replacement for Dirac operators.
These do not only come with a Riemannian metric $g$ but also a second fundamental form $K$, describing the first order change of the metric. For physical reasons the pairs $(g, K)$ arising on such hypersurfaces are expected to satisfy a certain inequality -- the dominant energy condition -- that generalizes the condition of non-negative scalar curvature if $K = 0$. As for non-negative (or
positive) scalar curvature, index theoretic methods can be used to study the (strict) dominant energy condition. In this context Dirac-Witten operators serve as the appropriate replacement for Dirac operators.
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Type:Colloquium
Language:English
Category:Research
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Direct link to event:https://events.goettingen-campus.de/event?eventId=25468
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