LGPortrait of Luca Giudici

Luca Giudici

PhD student in Mathematics · UniDistance Suisse

I'm a PhD student in mathematics, advised by Thomas Mettler. I started my PhD in September 2025, after a BSc and MSc in Mathematics at ETH Zürich.

My research is in differential geometry and geometric analysis, with a focus on projective structures on surfaces.

Interests: projective and conformal geometry · Riemann surfaces · geometric analysis · dynamical systems.

Theses

Service

Teaching

Teaching assistant for the following courses:

Education

Mathematical toys

A random tree

A uniformly random tree (root marked by a dot), grown from the random walk excursion drawn underneath: each step up adds a new edge, each step down walks back towards the root. As the number of vertices grows, suitably rescaled random trees converge to Aldous' continuum random tree, the starting point for the Brownian map.

The Bolza surface

Drag to move through the hyperbolic plane. Regular octagons with all angles equal to π/4 tile the Poincaré disk, eight meeting at every corner. Gluing opposite sides of the highlighted octagon (matching colours ) gives the Bolza surface, the most symmetric closed surface of genus 2.

Outside of mathematics

When I'm not doing mathematics, you'll most likely find me out running.

Luca running in a race along a path lined with trees and reeds
Greifenseelauf 2026