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Title:
Deligne-Lusztig theory: examples and applications
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Abstract:
Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over finite fields is encoded in the geometry of a natural "partition" of flag varieties. Recent developments have revealed rich connections between Deligne-Lusztig varieties and geometry studied in number-theoretic contexts. In this lecture series, we give an example-based tour of these ideas, focusing on how to extract concrete information from theory.
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