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Abelianization and its $q$-deformation
Mathematical Physics SeminarSpeaker: | Andrew Neitzke, Yale University and University of Texas, Austin |
Related Webpage: | https://web.ma.utexas.edu/users/neitzke/ |
Location: | 2112 MSB |
Start time: | Fri, Dec 6 2019, 11:00AM |
I will describe joint work in progress with Fei Yan, concerning a new geometric construction which quantizes the “abelianization” map between moduli spaces of flat $GL(N)$-connections on a surface $C$ and flat $GL(1)$-connections on spectral covers of $C$. The physical context of the construction is the study of framed BPS states in $N=2$ supersymmetric field theories. The construction extends and reinterprets previous work of Bonahon-Wong, Gabella, and Galakhov-Longhi-Moore. A byproduct is a new scheme for computing specializations of the HOMFLY polynomials of links.