Arithmetic geometry of representation spaces

Bailey Whitbread (University of Queensland)

Wednesday 20th September, 2023 16:00-17:00 Maths 110


Representation spaces are built out of homomorphisms from the fundamental group of a surface to an algebraic group. These spaces are related to many abstract and physical topics, including Yang-Mills equations, Hitchinin's equations, the P=W conjecture and mirror symmetry. 

In general, representation spaces are not well-understood. The most is known when the algebraic group is the general linear group, and the surface is orientable and punctured. This is largely due to the seminal work of Hausel, Letellier, and Rodriguez-Villegas.
In this talk, we will see new results regarding the geometry and topology of representation spaces associated to reductive algebraic groups. This is joint work with Masoud Kamgarpour and GyeongHyeon Nam, building on work done with Anna Puskás during her time in Australia. 

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