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
16/06/2026, 14.30, Sala S, Deparment of Mathematics "G. Peano" , Università di Torino,
Constant mean curvature foliations of almost-Fuchsian manifolds
Abstract: Quasi-Fuchsian groups have been the subject of extensive study since the 1890s. By naturally acting on 3-dimensional hyperbolic space, they describe a wide class of complete, infinite-volume hyperbolic 3-manifolds. Their properties have played a crucial role in Thurston's hyperbolization theorem and, more generally, in the study of the geometry and topology of 3-manifolds. Following Uhlenbeck, we say that a quasi-Fuchsian manifold is almost-Fuchsian if it contains an incompressible minimal surface with principal curvatures between -1 and 1. A conjecture by Thurston asserts that any almost-Fuchsian manifold admits a foliation by constant mean curvature (CMC) surfaces.
In this talk, I will describe a result from an upcoming joint work with Tien Nguyen, Andrea Seppi, and Jean-Marc Schlenker, where we determine explicit conditions on the first and second fundamental forms of the minimal surface of an almost-Fuchsian manifold that guarantee the existence of a CMC foliation.
19/06/2026, 10.30, Sala S, Deparment of Mathematics "G. Peano" , Università di Torino,
Geometrizing surface group representations
Abstract: The Teichmuller space T(S) of a closed surface S is a moduli space where each point represents a hyperbolic metric on the surface S. Interpreted appropriately, each of these hyperbolic metrics is encoded by the holonomy representation of the fundamental group of S to PSL(2,R), the group of isometries of the hyperbolic plane. This talk concerns a similar story with the Lie group PSL(2,R) replaced by the exceptional split real Lie group G_2’ of type G_2. That is, we shall “geometrize” surface group representations to G_2’ as holonomies of some (explicitly constructed) locally homogenous (G,X)-manifolds. Along the way, we encounter pseudoholomorphic curves in a non-compact pseudosphere that carry a (T,N,B)-framing analogous to that of space curves in Euclidean 3-space. These curves play a key role in the construction. Time permitting, we discuss how this specific G_2’ recipe relates to a broader construction that unifies other approaches to geometrize representations.
FORTHCOMING TALKS
25/06/2026, 14.30, Sala S, Deparment of Mathematics "G. Peano" , Università di Torino, Prof.ssa Catherine Searle.