Thursday 28 January 2021, 12:45-13:15 via zoom
Salvatore Floccari (RU)
The Mumford-Tate conjecture for hyper-Kähler varieties
he study of algebraic varieties is a very complicated subject. As dimension increases, our intuition can only be misleading. To get a grasp on such rich topic, algebraic geometers rely on cohomology theories. In my talk, I will consider two such theories: associated to an algebraic variety we have on the one hand a Hodge structure and on the other hand a Galois representation. They reflect geometric and arithmetic properties respectively. The Mumford-Tate conjecture predicts that these two invariants contain the same information; this is most remarkable due to the very different nature of these objects. I will conclude presenting my recent work which establishes the Mumford-Tate conjecture for an important class of higher dimensional algebraic varieties, called hyper-Kähler varieties.