Deadline: 15 nov 2026
As part of the newly financed PRIN project “The interplay of geometry and topology in the study of manifolds and groups” two to three postdoc positions will be advertised in Bologna to start between January 1st and November 1st 2027.
The potentially interested candidates should return the attached form per email to beatrice.pozzetti {at} unibo.it no later than November 15 as a single pdf not longer than three pages renamed "Surname.pdf".
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The project “The interplay of geometry and topology in the study of manifolds and groups”, is inspired from Thurston’s vision and builds on the multifaceted role of hyperbolic geometry in modern mathematics. It explores the interplay between geometry and topology, and their deep connections with geometric group theory, dynamics and differential geometry. We seek new examples of manifolds with interesting geometry, and obstructions thereof; we study the interplay between special submanifolds, topology and dynamics; we extend dynamical quantities from (hyperbolic) manifolds to finitely generated groups and find examples that extremize dynamical quantities; and we explore constraints that geometry imposes on homology and more generally topology.
The project is articulated in 4 macroareas (low dimensional geometry and topology, analytic techniques, discrete groups and dynamics, co-homological techniques), each addressing concrete problems that are central in modern geometric topology, and are strongly connected with recent advances in hyperbolic geometry. In Bologna node we will construct new examples of convex projective manifolds and hyperbolic manifolds of dimension 5, and study their topology, we will develop topological constructions in dimension 3 and 4 such as singular fibration and branching, we will study special submanifolds in the context of higher Teichmüller theory, we will study dynamical quantities inspired from hyperbolic geometry, such as the entropy, in contexts arising from geometric group theory and discrete subgroups of Lie groups, also using random walks techniques, and we will develop (co)homological invariants coming from bounded cohomology, simplicial volume and L2 invariants.
The researchers involved in Bologna node are:
Bologna: Cattabriga, Francaviglia, Marchese, Moraschini, Riolo, Pozzetti,
Modena: Casali, Cristofori,
Trieste: Mecchia, Zuddas