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Graded geometry in physics: above and beyond
19.4.2018, 16:15 - 17:15
Speaker:Dr. Vladimir Salnikov, La Rochelle University, France
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
In this talk I will recall various instances of graded geometry, appearing naturally
in some fields of classical differential geometry (Poisson, Dirac, equivariant theory...).
I will also explain that this is a convenient language for theoretical physics (sigma models,
gauging, symmetries of functionals...).

The key idea for physics is that one can reformulate the property of gauge
invariance in the language of equivariant Q-cohomology. This permits to exhibit
obstructions to gauging using a nice geometric picture, and describe the
symmetries of some sigma models, including the Dirac sigma model, which is
universal in the space-time dimension 2. The formalism can be also applied to
supersymmetric theories.

Time permitting, I will also sketch the direction of some work in progress related
to studying coupled mechanical systems. Generalized geometry, and in particular
Dirac structures, turn out to be useful in the context.
I will not assume any preliminary knowledge of graded geometry or theoretical physics
from the audience.
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Host:Prof. Dr. Chenchang Zhu
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