Activities

Selected talks

• Hyperbolic triangle chains and finite mapping class group orbits. Painlevé Seminar (online) [talk]
• Complex Projective Spaces Via Surface Groups Representations. Symplectic Zoominar, Institute for advanced studies [video].
• The two natures of components of character varieties. Topology Seminar, University of Iowa [talk].
• On remarkable representations of the fundamental group of a punctured sphere into $\mathrm{PSL}(2,\mathbb{R})$. Topology Seminar, University of Bristol [talk].

Workshops (co)organized

• Character varieties under the lens of Hodge theory. MPI Leipzig, May 2026 [web page]

  Abstract: Character varieties of surface groups are rich geometric objects lying at the intersection of topology, representation theory, and complex geometry. This workshop explores character varieties through the lens of Hodge theory, with a particular emphasis on complex variations of Hodge structures and their incarnation via nonabelian Hodge theory. Beginning with an introduction to polarized complex variations of Hodge structures, the workshop develops the correspondence between Hodge-theoretic data, Higgs bundles, and surface group representations. We will investigate how the C*-action on Higgs bundle moduli spaces detects representations arising from variations of Hodge structures, leading to geometric and dynamical applications to character varieties of closed and punctured surfaces. Topics include branched hyperbolic structures, compact components of relative character varieties, Hodge groups and their classification, and rigidity phenomena such as the Corlette–Simpson alternative. The workshop aims to make Hodge-theoretic techniques accessible while highlighting recent advances and open problems at the interface of Hodge theory and character varieties.

• Workshop on Interplay between symplectic geometry and cluster theory. IWH Heidelberg, January 2023 [web page]

  Abstract: Cluster algebras were introduced by Fomin and Zelevinsky in 2000 in the context of Lie theory. In the last twenty-two years the theory of cluster algebras gave life to several fascinating applications between different fields of mathematics such as quiver representations, Calabi-Yau categories, Teichm”uller theory, Poisson geometry, and many others.
  An interesting example stems from the work of Vianna, where a connection between Markov triples and not Hamiltonian isotopic Lagrangian tori is established. Motivated by this result, we would like to further understand the relations between cluster structures, quiver representations and almost toric fibrations.
  The aim of this workshop was to gain a deeper understanding of these interplay thanks to three mini-courses held by experts as well as some research talks. The IWH will provide us with a charming environment for discussions towards further explorations and perspectives.

• Young Researcher’s Workshop on Positivity in Lie Groups. IWH Heidelberg, January 2022 [web page] [proceedings]

  Abstract: The aim of this workshop was to understand the notion of total positivity and Theta-positivity and how it relates to Higher Teichmüller theory. Theta-positivity is a notion of positivity in semisimple Lie groups and was recently introduced by Guichard and Wienhard in Positivity and higher Teichmüller theory as a generalization of Lusztig’s total positivity.