[Geom., Alg. & Phys.] Skein Algebras of Surfaces and Quantum Symplectic Doubles
ABSTRACT
Skein algebras serve as the algebraic quantizations of character varieties of surfaces with respect to the Atiyah-Bott-Goldman Poisson bracket. They share deep connections with quantum groups, quantum Teichmüller space, and quantum cluster algebras.
This talk will begin with an accessible introduction to the theory of skein algebras. We will then investigate the relationship between the SL_n-skein algebra of a closed surface S and the quantum symplectic double of a punctured surface obtained by cutting S in half.
This talk is based on joint work with W. Bloomquist, H. Karuo, A. Poudel, and Z. Wang. (Zoom: Meeting ID: 890 4516 0531, Passcode: 079802, link: https://kias-re-kr.zoom.us/j/89045160531?pwd=OSCYO85Ra4R8CcfTl7wvmmtb8j1GOZ.1) (https://sites.google.com/view/gapkias)
