About:

I am a junior Assistant Professor  in Mathematics at the University of Bologna. Before that I was a Postdoctoral Researcher at Southampton were my mentor was Bernhard Koeck. I received fundings  from a LMS Early Career Fellowship and the EPSRC as a winner of a prestigious EPSRC Doctoral Prize .

As a pure mathematician, I work in a field called algebraic K-theory, a fascinating subject bridging algebra, geometry and topology. This is one of the purest, newest and technically most demanding fields of pure Mathematics and will certainly play a crucial role in the area over the next few decades. 

More recently, as a pure/applied mathematician an I am also working in the field of Geometric Deep Learning, where, collaborating with both academics and private companies I study cutting edge techniques to solve real world problems coming from many different areas (e.g. biotech).

I got a PhD in Mathematics in 2019 from the University of Warwick, my advisor was Marco Schlichting.

Research Interests:

Pure Maths:

• Algebraic and Hermitian K-theory.

• K-theory of form categories.

• Algebraic geometry and homotopy theory.

• Homotopical methods in algebraic geometry: A1-homotopy theory, motivic cohomology, homotopical algebra and derived categories .

• Derived Algebraic Geometry.

• Geometric Deep Learning and its interlinks with the above.

Applied Maths:

• Machine Learning and Artificial Intelligence.

• Geometric Deep Learning and its real world applications especially in the fields of medicine, pharmacology and biotechnology.

Works:

Pure:

• F. Zanchetta, K-theory of forms via binary complexes. In preparation.

• B. Köck, F.Zanchetta, Comparison of Exterior Power Operations on Higher K-Theory of Schemes. Submitted. Preprint. (pdf ).

• F. Zanchetta, Unstable operations on K-theory for singular schemes.  Advances in Mathematics, Volume 384, 2021.(link   pdf )

• F. Zanchetta, Embedding Divisorial Schemes into Smooth Ones.  Journal of Algebra Vol.552:86-106, 2020. (link)(pdf)

• F. Zanchetta, Operations in (Hermitian) K-Theory and related topics.  PhD thesis, 2019.(pdf)

• R. Fioresi and F. Zanchetta Representability in Supergeometry. Expo. Math.  Vol.35 (3) , 2017. (link)(pdf)

Mathematics of Deep Learning:

• R. Fioresi, F. Zanchetta, Deep Learning and Geometric Deep Learning: an introduction for mathematicians. International Journal of Geometric Methods in Modern Physics, to appear. (link)

• M. Lapenna, F. Faglioni, F. Zanchetta, R.Fioresi, Geometric Deep Learning: a temperature based analysis of graph neural networks. Proceedings of GSI 23 (link) .

Applied:

• Michela Lapenna, Athanasios Tsamos, Francesco Faglioni, Rita Fioresi, Ferdinando Zanchetta, Giovanni Bruno, Geometric Deep Learning for enhancedb quantitative analysis of Microstructures in X-ray Computed Tomography Data. Submitted

• A. Simonetti, F. Zanchetta, Graph Neural Networks and Time Series as Directed Graphs for Quality Recognition. Submitted. Preprint (link ).

• F. Zanchetta, A. Simonetti, G. Faglioni, A. Malagoli and R. Fioresi, A Geometric deep learning approach to blood pressure regression. Extended abstract accepted to GeoMedIA workshop 2022  (Link ). (Paper in Preparation)

• C. P. Coutinho, F. Zanchetta, A. Galzignato, M. Batista, G. Lari, A. Stefano, E. Borrelli, G. Savini, M. L. Cascavilla, F. Bandello, R. Fioresi, P. Barboni, Machine Learning application in Visual Field Loss for Dominant Optic Atrophy.  Submitted.

• F. Zanchetta, A. Simonetti, G. Faglioni, A. Malagoli and R. Fioresi, A Geometric deep learning approach to ECG and PPG quality recognition. In progress.

• J. Bertozzi, K. Carlin, I. Di Silvestro, R. Fioresi, A. Ghetti, B. Krause, G. Perini, F. Zanchetta, Gene Selection for RNA HTT and Neuropathic Pain vs no Pain Classification, based on a Machine Learning approach. In preparation.