Alessandro Tamai
Ph.D. student at SISSA in Geometry and Mathematical Physics as member of the Real Geometry Group, under the supervision of Antonio Lerario.
Contacts
email: atamai@sissa.it
office: room 416
Research Interests:
With a background in differential topology and machine learning, my current research focuses on applying differential topology, real algebraic geometry, and Morse theory to statistical learning theory, especially in manifold learning and neural network theory.
More broadly, the following informal list collects results and topics I’ve encountered during my career and found most fascinating. In classical mechanics, the Liouville–Arnold theorem and the KAM theorem; in random geometry and probability, the Monte Carlo methods , Kac–Rice formula, random matrix theory, and the theory of spin glasses—especially the Parisi replica method and its connections with information theory and machine learning; in symplectic and differential geometry, the Harish–Chandra–Itzykson–Zuber integral, the Duistermaat–Heckman theorem, and Cartan’s theory of connections on principal bundles; and in geometry and topology, the Weyl tube formula for real and Kähler manifolds, the classification of semisimple Lie algebras, and the Morse theory of critical points.
Some specific papers: Testing the Manifold Hypothesis by C. Fefferman, S. Mitter, and H. Narayanan, Can One Hear the Shape of a Drum? by M. Kac, On the Total Curvature of Knots by J. Milnor, and Real Algebraic Manifolds by J. Nash.
Where I am (right now):
SISSA research center in Trieste (Italy).
