Stefano Riolo

mathematician based in Bologna, working in geometry and topology

email: stefano!.!riolo!@unibo.it

institutional web page here (teaching, etc.)

my research mainly focuses on interactions between the geometry and topology of manifolds. I'm particularly interested in hyperbolic manifolds and deformations of hyperbolic structures, especially in dimension four. here are my works:

papers

• A small cusped hyperbolic 4-manifold
Bull. Lond. Math. Soc. 56:1 (2024) 176-187 journal arXiv

• The signature of cusped hyperbolic 4-manifolds
with Sasha Kolpakov and Steve Tschantz
Int. Math. Res. Not. IMRN 2023:9 (2023) 7961-7975 journal arXiv

• Character varieties of a transitioning Coxeter 4-orbifold
with Andrea Seppi
Groups Geom. Dyn. 16:3 (2022) 779-842 journal arXiv

• A small closed convex projective 4-manifold via Dehn filling
with Gye-Seon Lee and Ludovic Marquis
Publ. Mat. 66:1 (2022) 369-403 journal arXiv

• Geometric transition from hyperbolic to anti-de Sitter structures in dimension four
with Andrea Seppi
Ann. Sc. Norm. Super. Pisa Cl. Sci. XXIII:1 (2022) 115-176 journal arXiv

• Embedding non-arithmetic hyperbolic manifolds
with Sasha Kolpakov and Leone Slavich
Math. Res. Lett. 29:1 (2022) 247-274 journal arXiv

• Convex plumbings in closed hyperbolic 4-manifolds
with Bruno Martelli and Leone Slavich
Geom. Dedicata 212:1 (2021) 243-259 journal arXiv

• Compact hyperbolic manifolds without spin structures
with Bruno Martelli and Leone Slavich
Geom. Topol. 24:5 (2020) 2647-2674 journal arXiv

• Many cusped hyperbolic 3-manifolds do not bound geometrically
with Sasha Kolpakov and Alan Reid
Proc. Amer. Math. Soc. 148:5 (2020) 2223-2243 journal arXiv

• Counting cusped hyperbolic 3-manifolds that bound geometrically
with Sasha Kolpakov
Trans. Amer. Math. Soc. 373:1 (2020) 229-247 journal arXiv

• New hyperbolic 4-manifolds of low volume
with Leone Slavich
Algebr. Geom. Topol. 19:5 (2019) 2653-2676 journal arXiv

• Hyperbolic Dehn filling in dimension four
with Bruno Martelli
Geom. Topol. 22:3 (2018) 1647-1716 journal arXiv

• Spines of minimal length
with Bruno Martelli, Matteo Novaga, and Alessandra Pluda
Ann. Sc. Norm. Super. Pisa Cl. Sci. XVII:3 (2017) 1067-1090 journal arXiv

thesis

• Cone-manifolds and hyperbolic surgeries
supervisor Bruno Martelli, University of Pisa (2017) link

papers in preparation or work in progress (tentative titles)

• Dehn filling all the cusps of a hyperbolic 4-manifold
with Gye-Seon Lee, Ludovic Marquis, and Tomoshige Yukita

• Filling and drilling complex hyperbolic surfaces
with Pietro Sabatino

• Convex projective 4-manifolds
with Andrea Seppi and Leone Slavich

the animations (taken from here) represent the six regular 4-polytopes, which are four-dimensional analogues of the more familiar Platonic solids. my favourite one is the 24-cell:

if you've scrolled this far, maybe you're bored, or you're really looking for something more. in either case, here you are some songs (in Italian):

• Poloniaviolenta - Capire, mantra while doing or preparing a lesson

• Antonio Freno - Vorrei costruire un oggetto, research

• Poloniaviolenta - Vittime, against the war