Colloquium
Speaker: Joel Kamnitzer (University of Toronto)
"Categorical actions of sl(2) and equivalences of categories"
Time: 14:30
Room: MC 108
Actions of the Lie algebra sl(2) on vector spaces arise naturally in
combinatorics, geometry, and algebra. Such an action consists of a sequence
of vector spaces with linear maps between them satisfying certain relations.
From this perspective, one can define an action of sl(2) on a category to be
a sequence of categories with functors between them satisfying certain
relations. Such actions were studied by Chuang-Rouquier in the context of
representations of the symmetric group in positive characteristic.
More recently, Cautis, Licata, and the speaker studied an action of sl(2)
where the categories involved were derived categories of coherent sheaves on
cotangent bundles to Grassmannians. Following the ideas of Chuang-Rouquier,
we used this sl(2) action to construct an equivalence of derived categories
between different cotangent bundles of Grassmannians.
Mathematics Calendar 
Week of October 26, 2008
