Giovanni Luca Marchetti



I am a postdoctoral researcher at the Department of Mathematics of the Royal Institute of Technology (KTH) in Stockholm, Sweden.

I apply tools from pure mathematics (algebra, geometry, topology, ...) to machine learning and high-dimensional statistics. More specifically, I am interested in algebro-geometric aspects of deep neural networks, manifold/representation learning, geometric density estimation, and topological data analysis. Check these slides for a high-level presentation of my research so far.



Geometry ⊗ Deep Learning

Resources: CV,  Google Scholar,  GitHub,  X/Twitter,  LinkedIn




Publications

Below you can find a selection of my academic works, subdivided into topics. For a complete list, please visit my Google Scholar profile. The symbol * denotes equal contribution.

Algebraic Geometry of Deep Learning: these works explore the (algebraic) geometry of function spaces defined by neural networks.

Equivariant/Invariant Deep Learning: these works explore the interaction between symmetry and deep learning, ranging from the invariant theory of neural networks to equivariant representation learning, with applications to robotics.

Computational Geometry: these works concern high-dimensional Voronoi tessellations and Delaunay triangulations, with applications to density estimation and active learning.

Other: these works concern various topics in pure mathematics, e.g., category theory and combinatorics.

Thesis: I obtained my doctoral degree from KTH in 2024 under the supervision of Prof. Danica Kragic. Below you can download the thesis.