PIRSA:25030180 Scientific Series Mathematical physics

DOI10.48660/25030180

Series: Mathematical Physics

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}}
}

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.

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