Work in Progress

with Michael Werman: applications of Riemannian geometry and group theory to image processing
with Kiran S. Kedlaya, Bjorn Poonen & Michael Rubinstein: combinatorial and number-theoretic properties of point configurations
with Maria Dostert, Oleg Musin, Philippe Moustrou, Fernando M. de Oliveira: optimal geometric configurations of spheres in spaces of constant sectional curvature
with Nikolay Bogachev, Leone Slavich & Misha Belolipetsky: arithmetic and quasi-arithmetic hyperbolic Coxeter polytopes, stabilisers and centralisers in (quasi-) arithmetic lattices
with Alan W. Reid, Stefano Riolo, Leone Slavich, Michelle Chu: geometric cobordisms of hyperbolic manifolds, embeddability of codimension one manifolds
with Alexey Talambutsa: growth rates of Coxeter groups and Artin groups, and their number-theoretic properties, free groups and semigroups
with Laura Ciobanu, Rémi Bottinelli, Laura Grave de Peralta: enumeration problems for triangulations, polytopal decompositions and other geometric objects
with Jun Murakami: correspondences between hyperbolic volumes and quantum invariants of graphs, links and knots
with Nikolay Abrosimov, Sasha Mednykh, Sinai Robins: hyperbolic, spherical and Euclidean volumes of manifolds and orbifolds, and their number-theoretic properties