Ph.D. Courses 2023 – 2024

Below is a list of Ph.D. courses that will be taught during the academic year 2023-2024.

Fall/Winter Term

p-adic Galois Representations

Tamás Szamuely

Theory of currents

Giovanni Alberti

Winter/Spring Term


Riccardo Benedetti

Contact Geometry

Paolo Lisca

Deep Learning Theory

Andrea Agazzi

Dynamics of Complex Systems

Stefano Galatolo

Nonlinear Analysis

Marco Gipo Ghimenti

Quotients and Moduli Spaces

Francesco Sala
Mattia Talpo

“Moduli spaces” are spaces whose points classify some algebro-geometric (or even topological, etc.) objects of interest. The most famous example is probably the moduli space of complex algebraic curves (i.e. compact Riemann surfaces), already envisioned by Riemann in the mid-800s. The study of the geometry of moduli spaces has been one of the central topics in algebraic geometry, geometric representation theory, etc, for a few decades now, and their construction often requires taking a quotient (i.e. orbit space) of the action of an algebraic group on some algebraic variety. This is often done via the machinery of GIT (geometric invariant theory), although there are more recent alternatives, that make use of algebraic stacks.

The first part of the course will cover some basics about moduli spaces and their construction, illustrated alongside relevant examples, and focusing on GIT and/or on the use of algebraic stacks. The second part will be devoted to examples.

The decision about the focus of the course and what examples to cover will be taken after a preliminary meeting with the prospective attendees of the course, which will take place presumably during November/December 2023.

Storia, tecnologie e teorie: strumenti in e per la ricerca in didattica della matematica

Lecturers: TBA

Topics in Modeling and Analysis in Materials Science

Cyrill Muratov
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