Research Group in
Real Geometry

I am interested in various aspects of real algebraic and differential geometry, and their interactions with convex geometry, metric geometry, topology, singularity theory and applications.

My main interests are on applications of metric geometry, real algebraic geometry and Morse theory in machine learning. Others cover differential topology, Riemannian and subRiemannian geometry and Lie groups.

I am currently investigating the interplay between optimal transport and algebraic geometry, starting with Wasserstein distances on spaces of polynomials.

The ideal member is curious and genuinely interested in mathematics. They are open to exploring different areas (with a taste for geometry), comfortable with informal discussions, and willing to contribute their knowledge while learning from others. Flexibility and an interest in the group's diverse directions are important.

I am interested in Riemannian geometry. I started out working in nearly Kähler geometry. I then explored the connections with spin geometry and GKM theory. I recently got interested in the geometry and topology of submanifolds with constant r-th mean curvature. Currently I work on topics in G_2 and integral geometry.

I am interested in the properties of the zonoid ring with a view towards a real version of Schubert calculus.

I am interested in metric properties of real algebraic varieties. Currently my focus is on properties of distance functions from algebraic subvarieties in non-linear settings, e.g. in Grassmann varieties. Other topics of interest include random algebraic geometry, random tensors and typical ranks of real tensors.

I am currently working between approximation theory and topology. Specifically, I am studying a condition number approach to obtain bounds for the Betti numbers of sets defined by smooth equations. In this context, the condition number has a similar role to that of the degree in the semi-algebraic setting.  

My curiosity is directed towards differential geometry, often through the lenses of a symplectic approach. I am actually focusing, at the moment, in symplectic topology, but I am eager to expand my knowledge in neighbouring areas of Mathematics.