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Root system pattern avoidance, rational smoothness, and inversion arrangements
Student-Run Research| Speaker: | William Slofstra, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Dec 4 2013, 12:10PM |
Description
A theorem of Lakshmibai-Sandhya states that smooth Schubert varieties
in the flag variety of a vector space correspond to permutations which avoid
two patterns. Billey and Postnikov introduced the notion of root-system pattern
avoidance to extend this criterion to Schubert varieties of arbitrary type.
Their criterion requires checking patterns in a finite number of spectral root
systems. I will explain how to get a root-system pattern avoidance criterion
for freeness of inversion hyperplane arrangements, and talk about some
further problems in this area.