Date: Wednesday, March 20, 2013
Location: 3088 East Hall (4:00 PM to 6:00 PM)
Title: The McKay correspondence
Abstract: Let $G$ be a subgroup of $SL_n(\mathbb{C})$. The classical McKay correspondence relates the representation theory of $G$ with the structure of a minimal resolution of $\mathbb{C}^n/G$. For $n=3$, Bridgeland, King, and Reid used categorical techniques to show that $\mathbb{C}^n/G$ has a distinguished crepant resolution $G$-Hilb.
In the first half I will demonstrate a technique due to Craw and Reid for constructing $G$-Hilb in the toric case (when $G$ is abelian). In the second half I will introduce derived equivalences and their relation to birational geometry, with the $3$ dimensional McKay correspondence as a motivating example.
Speaker: Morgan Brown
Institution: UM
Event Organizer:
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