Speaker: Sam Panitch
Abstract: Fix an ideally triangulated surface S. The 2d quantum trace map, invented by Bonahon and Wong, connects two different quantizations of the character variety of S: the sl_2 skein algebra and quantum Teichmüller space. The UV-IR map, developed from a more physical point of view by Nietzke and Yan, maps the gl_2 skein algebra of S to the gl_1 skein algebra of a specific double cover associated to a spectral network on S. With a certain choice of this spectral network, it turns out that these two maps are essentially equivalent. In this talk, we will make sense of this statement. A similar comparison was carried out by Kim, Lê, and Son.
Furthermore, we will upgrade this statement to ideally triangulated 3-manifolds. That is, we will show that the UV-IR map, when applied to a specific spectral network associated to an ideal triangulation, is essentially equivalent to the 3d quantum trace map (P. and Park, and Garoufalidis and Yu). This is joint work with Sunghyuk Park.
Time: 2:00 – 3:00 PM, Feb. 26, Wednesday
Location: R1310 at SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
Zoom Meeting No.: 423 317 8953 (Passcode: SIMIS)
English 
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