The Bruhat order on clans, and applications to local structure of symmetric orbit closures
Benjamin Wyser (Grenoble)
What 


When 
Nov 19, 2015 from 10:15 am to 11:45 am 
Where  Mainz, 05432 (Hilbertraum) 
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I will describe a result
of mine which explicitly determines the ``Bruhat order'' (or closure
containment order) on the orbits of the symmetric subgroup $GL_p \times GL_q$
on the flag variety $GL_{p+q}/B$, relative to their parametrization by
combinatorial objects known as ``clans''. I will give some applications
of this theorem, surveying some recent work of myself joint with Alexander Woo
and Alexander Yong. Specifically, I will relay how the theorem can be
used to study:
1. The local structure and singularities of such orbit closures (via
``patch ideals'');
2. Cohomological invariants (via Gr\"{o}bner geometry of ``matrix
orbit closures"); and
3. Local isomorphisms of different orbit closures whose combinatorial
parameters are related by pattern embeddings (via ``MarsSpringer
varieties").