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2023年7月25日(火) 17:30~19:00
i-Siteなんば S1での対面およびZoomのハイブリッド形式
Quantum duality maps, skein algebras and their ensemble compatibility
In the context of quantum Teichmüller theory, conjectured were the existence of quantizations of trace functions of Teichmüller spaces and some expected properties. A construction of such quantizations, called the quantum duality maps, was given for punctured surfaces by Allegretti–Kim and for marked disks by Allegretti. Allegretti–Kim’s strategy was based on skein algebras and Bonahon–Wong’s quantum trace maps. One of the expected properties is the positivity of structure constants of the images of the quantum duality maps, so-called the positivity conjecture. Although Mandel–Qin showed the coincidence of theta bases and their quantum duality maps and the positivity conjecture as a corollary, it is still important to understand the positivity with explicit formulas of structure constants in terms of skein algebras. In the talk, we try to understand the positivity of structure constants using reduced stated skein algebras. This is a joint work with Ishibashi Tsukasa (Tohoku University)