Wednesday 13 May 2026, from 2 pm in Room U9-14 (U9 Building - Viale Dell’Innovazione 10, Milano), Carlo Collari (University of Firenze) and Christian El Emam (University of Torino) will give the following talks
Speaker: Carlo Collari
Title: Polynomial invariants of strongly involutive links
Abstract: Distinguishing links in the three-sphere is a central problem in low-dimensional topology. Polynomial link invariants, such as the HOMPTFLY polynomial, are primer examples of powerful yet computable invariants. In this talk I will present an analogue of the HOMPTFLY polynomial for strongly involutive links -- i.e. links with an involution of the three-sphere that leaves the link invariant but reverses the orientation of each component. I will compare this polynomial invariant to other known invariants of strongly involutive links. As an application, I will show how this polynomial can be leveraged to distinguish inequivalent links with the same HOMPTFLY polynomial.
Speaker: Christian El Emam
Title: Minimal surfaces and Higher Teichmüller Theory
Abstract: Throughout the last century, Teichmüller theory has built bridges between different perspectives in the study of surfaces, connecting the theories of Riemann surfaces, hyperbolic metrics, and Fuchsian representations of the fundamental group into PSL(2,R). One of the remarkable features of this interplay is that it naturally endows Teichmüller space with several compatible geometric structures, including a Kähler structure. More recently, the so-called Higher Teichmüller theory aims to extend this picture, seeking geometric interpretations to representations into higher-rank Lie groups. In this setting, the relation with the geometry of minimal surfaces in locally symmetric spaces has proved to be particularly fruitful.
After introducing the main notions, in this talk I will present a "complex" geometric approach to Higher Teichmüller theory, especially for rank equal to 2. In particular, I'll show that, in a similar spirit as in Teichmüller theory, different geometric viewpoints are compatible, allowing to define a pseudo-Kähler structure on Hitchin components and to generalize Bers' Simultaneous Uniformization Theorem.
This is joint work with Nathaniel Sagman.
All interested are invited to participate
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