Giovanni Luca Marchetti
I am a postdoctoral researcher at the Department of Mathematics of the Royal Institute of Technology (KTH) in Stockholm, Sweden.
My research focuses around applications of 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.
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Publications
Below you can find a selection of my academic works, subdivided into topics. For a complete list, please visit my Google Scholar profile.
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.
