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Hypertoric category O

SPEAKER: Nicholas Proudfoot

TITLE: Hypertoric category O

ABSTRACT: Bernstein, Gelfand, and Gelfand introduced a certain category of representations of a Lie algebra that’s so awesome that it is known simply as “category O”. This category has been extensively studied from three different perspectives, which I’ll call the algebraic, geometric, and combinatorial. All of these perspectives have been extremely useful for proving lots of neat stuff about category O. Recently, my friends and I have defined something called “hypertoric category O”, which takes its input data from linear algebra (hyperplane arrangements) rather than representation theory. Like the BGG category O, our category can be studied from any of three beautiful perspectives, and we can prove analogues of much of the aforementioned neat stuff. I will tell you as much about it as I have time for.