Derived categories of moduli spaces of stable rational curves  
-- Ana-Maria Castravet, December 1, 2017

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A question of Orlov is whether the derived category of the Grothendieck-Knudsen moduli space M(0,n) of stable, rational curves with n markings admits a full, strong, exceptional collection that is invariant under the action of the symmetric group S_n. I will present several approaches towards answering this question. In particular, I will explain a construction of an invariant full exceptional collection on the Losev-Manin space. This is joint work with Jenia Tevelev.