Welcome to the website of the seminar organized by the Differential Geometry groups of Università di Torino and Politecnico di Torino.
For any information, please send an e-mail to dgseminar.torino@gmail.com.
The talks will take place either at the Deparment of Mathematics "G. Peano" (Università di Torino) or at the Department of Mathematical Sciences "G.L. Lagrange" (Politecnico di Torino).
NEXT TALK
04/12/2025, 2.30 AM, Aula C, Dipartimento di Matematica "G. Peano", Università di Torino
The cohomogeneity one Einstein ODE
Abstract: For a Riemannian manifold (M^n,g) the Einstein equation Ric(g)=λ⋅g is (weakly) elliptic. Assuming symmetry this second order PDE simplifies: If the Riemannian manifold is homogeneous, then the Einstein equation turns into an algebraic equation. If the Riemannian manifold is of cohomogeneity one, then the Einstein equation becomes a highly non-linear dynamical system, the cohomogeneity one Einstein ODE.
In this talk we will present general structure results for the cohomogeneity one Einstein ODE.
FORTHCOMING TALKS
09/12/2025, 2.30 AM, Sala S, Dipartimento di Matematica "G. Peano", Università di Torino
Christian El Emam (Torino)
Minimal surfaces and higher Teichmüller theory
Abstract:Throughout the last century, Teichmüller theory established a profound bridge between different perspectives in the study of surfaces, connecting Riemann surfaces, hyperbolic metrics, and Fuchsian representations of the fundamental group into PSL(2,R). The interplay between these points of view is deep, and it allows to construct compatible geometric structures on Teichmüller space, such as a Kähler structure.
In recent decades, higher Teichmüller Theory aims to generalize this picture, seeking geometric interpretations for representations in higher rank Lie groups. In this setting, the connection with the study of minimal surfaces inside locally symmetric spaces has proved to be very successful.
After introducing the fundamental concepts, in this talk I will present a recent joint work with N. Sagman, where we use the notion of complex minimal surfaces to study this interaction. In particular, we establish a pseudo-Kähler structure on Hitchin components and generalize Bers' Simultaneous Uniformization Theorem for rank-2 lie groups, such as SL(3,R).