Seminar:
Colloquium
Event time:
Wednesday, October 2, 2024 - 4:00pm
Location:
KT 205
Speaker:
Hyun Kyu Kim
Speaker affiliation:
Korea Institute for Advanced Study
Event description:
For a punctured surface S and a split reductive algebraic group G such as SL_n or PGL_n, Fock and Goncharov (and Shen) consider two types of moduli spaces parametrizing G-local systems on S together with certain data at punctures. They show that these spaces have special coordinate charts, hence are birational to cluster varieties. Fock and Goncharov’s duality conjectures predict the existence of a canonical basis of the algebra of regular functions on one of these spaces, enumerated by the tropical integer points of the other space. I will give an introductory overview of this topic, briefly explain recent developments involving quantum topology and mirror symmetry of log Calabi-Yau varieties, and present some open problems if time allows.