PIRSA:25030180

Ideas in Multiplicative Non-abelian Hodge theory

Ong, M. (2025). Ideas in Multiplicative Non-abelian Hodge theory. Perimeter Institute. https://pirsa.org/25030180

Ong, Marielle. Ideas in Multiplicative Non-abelian Hodge theory. Perimeter Institute, Mar. 27, 2025, https://pirsa.org/25030180 

          @misc{ pirsa_PIRSA:25030180,
            doi = {10.48660/25030180},
            url = {https://pirsa.org/25030180},
            author = {Ong, Marielle},
            keywords = {Mathematical physics},
            language = {en},
            title = {Ideas in Multiplicative Non-abelian Hodge theory},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {mar},
            note = {PIRSA:25030180 see, \url{https://pirsa.org}}
          }

Marielle Ong University of Toronto

Talk numberPIRSA:25030180
DOI10.48660/25030180
Collection
Talk Type Scientific Series
Subject

Abstract

Non-abelian Hodge theory is a profound three-way equivalence between topological, smooth and holomorphic objects, i.e. representations of the fundamental group, flat connections and Higgs bundles. It is natural to explore a group-theoretic or multiplicative version — an enterprise that has been untaken by Soibelman, Kontsevich, Mochizuki and others. In this talk, we will review the current landscape of multiplicative non-abelian Hodge theory and discuss some outstanding questions.