Motivic Realization of Rigid Local Systems on Curves via Geometric Langlands

Explore the motivic realization of rigid local systems on curves through the geometric Langlands program in this advanced mathematics lecture from the Joint IAS/PU Arithmetic Geometry seminar. Delve into Simpson's conjecture regarding the characterization of local systems that arise in families of varieties, known as motivic local systems, and discover how this conjecture has been proven for curves with arbitrary reductive groups. Learn about the natural problem of identifying which local systems on complex varieties can be realized motivically, building upon Katz's earlier work for GL_n cases. Examine the proof methodology that utilizes the tamely ramified geometric Langlands program in characteristic zero to establish Simpson's conjecture for curves with any reductive group G. Gain insights into the classification of rigid G-local systems with appropriate conditions at infinity and understand the broader implications for smooth projective varieties. The presentation covers advanced topics in arithmetic geometry, algebraic geometry, and representation theory, making connections between local systems, motivic theory, and the geometric Langlands correspondence.