3:45 pm Tuesday, February 28, 2023
Junior Geometry: Higher Rank Uniformization by Charlie Reid in PMA 12.166
The uniformization theorem tells us that there is a unique hyperbolic hermitian metric on each Riemann surface of genus at least 2. Because the automorphism group of the hyperbolic plane is PSL(2,R), this ends up giving an identification of the Teichmuller space of a surface S (the space of isotopy classes of complex structures on S) with a component of the variety of PSL(2,R) local systems on S. I will explain this story in more detail, and talk about a conjectural generalization to SL(n,R) that I'm working on, together with Kydonakis, Nolte, and Thomas. Submitted by
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