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

**Lecturer:**

#### Theory of currents

**Lecturer:**

#### Winter/Spring Term

#### TBA

**Lecturer:**

#### Contact Geometry

**Lecturer:**

#### Deep Learning Theory

**Lecturer:**

#### Dynamics of Complex Systems

**Lecturer:**

#### Nonlinear Analysis

**Lecturer:**

#### Quotients and Moduli Spaces

**Lecturers:**

**Description: **

“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