ICTS:31203

Video URL

Canonical bases for moduli spaces of local systems related to higher Teichmüller spaces

Canonical bases for moduli spaces of local systems related to higher Teichmüller spaces

(2025). Canonical bases for moduli spaces of local systems related to higher Teichmüller spaces. SciVideos. https://youtube.com/live/SzImHsyd-48

Canonical bases for moduli spaces of local systems related to higher Teichmüller spaces. SciVideos, Feb. 23, 2025, https://youtube.com/live/SzImHsyd-48 

          @misc{ scivideos_ICTS:31203,
            doi = {},
            url = {https://youtube.com/live/SzImHsyd-48},
            author = {},
            keywords = {},
            language = {en},
            title = {Canonical bases for moduli spaces of local systems related to higher Teichm{\"u}ller spaces},
            publisher = {},
            year = {2025},
            month = {feb},
            note = {ICTS:31203 see, \url{https://scivideos.org/index.php/icts-tifr/31203}}
          }
Hyun Kyu Kim
Talk numberICTS:31203
Source RepositoryICTS-TIFR
Collection

Abstract

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. These moduli spaces yield versions of higher Teichmüller spaces, and are equipped with special coordinate charts, making them 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.