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Explore advanced concepts in algebraic geometry through this joint IAS/PU Arithmetic Geometry seminar lecture that examines the splinter property of affine Schubert varieties. Learn about the foundational work of Mehta and Ramanathan demonstrating that Schubert varieties are Frobenius split in positive characteristic, and discover Bhatt's recent proof that the full flag variety for GLn is a splinter using entirely different methodological approaches. Understand how these concepts extend to a generalization of Bhatt's result covering all Schubert varieties for all reductive groups, with methods that apply equally to affine Schubert varieties. Gain insights into the connections between these geometric objects and the Langlands program as well as representation theory of algebraic groups, presented through collaborative research with João Lourenço that bridges classical algebraic geometry with modern arithmetic geometric techniques.
