Tom Gannon, UCLA
A time tested strategy used to answer questions about the representation theory of a Lie group is to translate them to questions on the geometry of its quotients. After giving a survey of representation theory aimed at a broad audience, I will describe the theorems I have obtained using this strategy, including work which resolves a conjecture of Ginzburg—Kazhdan, work with Williams that proves a conjecture of Dancer—Hanany—Kirwan, work with Webster that proves a conjecture of Bourget—Dancer—Grimminger—Hanany—Zhong, and work with Ginzburg which resolves conjectures of Nadler and Ben-Zvi—Gunningham.