Materials

This page collects projects and academic reports produced during my undergraduate.

Theses

• Parameter Control for LeadingOnes on Enhanced State Spaces
  Master’s Thesis

  The thesis investigates optimal parameter control for randomized optimization algorithms using enriched state-space models, under the supervision of Prof. Carola Doerr (Sorbonne Université/CNRS) and Prof. Stefano Gualandi (University of Pavia).
  → Thesis (PDF) · Slides

• Ewens’ Sampling Formula and Applications to the Study of Biodiversity (Italian)
  Bachelor’s Thesis

  This thesis studies Ewens’ sampling formula and its applications to population genetics models, under the supervision of Prof. Emanuele Dolera.
  → Thesis (PDF) · Slides

Undergraduate Reports and Research Projects

• Research in Statistical Optimal Transport
  Ongoing research collaboration with Prof. Carlo Ciliberto (UCL) on entropic approximations of the Knothe–Rosenblatt rearrangement and Bayesian inference.
  (Status: work in progress)

• Submodularity for Distributionally Robust Optimization
  This report surveys the role of submodular functions in distributionally robust optimization, under the supervision of Prof. Angelos Georghiou and Prof. Rosario Paradiso.
  → Report (PDF)

• Statistical Study of Stochastic Optimization Problems
  This project investigated the statistical consistency properties of stochastic optimization problems, conducted at the Statistical Laboratory under the supervision of Prof. Qingyuan Zhao and Tobias Freidling.
  → Report (PDF)

• Internship Report at Sphaera
  This project consisted in the development of an algorithm for sports analytics combining neural networks and computer vision techniques, conducted at the startup Sphaera under the supervision of Dr. Mirko Messori and Dr. Giuseppe Marseglia.
  → Report (PDF)

Exam Projects

Some examinations during my studies included the preparation of a presentation or a written report. Relative materials are listed below.

Additional laboratory work and programming assignments developed during BSc and MSc courses are available on my GitHub profile:
→ github.com/gianlucacovini

PhD courses

• Machine Learning
  Optimal Transport for Generative Modeling

• Stochastic Processes
  Mean-field Schrödinger Problem

• Statistical Theory
  Merging Rate of Opinions via Optimal Transport on Random Measures

• Graph Theory
  Spectral Graph Theory and Discrete Poisson Equation: slides, report

• Julia Programming
  SlicedWasserstein.jl: a Julia package for sliced optimal transport and an application to clustering

• Optimization
  The Information Geometry of Optimization

• Optimal Transport
  The Gradient Flow Interpretation of the Fokker–Planck Equation

• Statistical Mechanics for Complex Systems
  Mean-Field Optimal Control

Master’s and Bachelor’s courses

• Statistical Methods for Physics
  Simulated Annealing: A Monte Carlo Algorithm for Non-convex Optimization

• Machine Learning
  Beans Classification

• Econometrics (Italian)
  Iscrizioni in scuole private

• Foundations of Data Science (Italian)
  SVD Randomizzata: un algoritmo per la riduzione della dimensionalità

• Optimization Algorithms and Models (Italian)
  Round-Based Public Transit Routing: un algoritmo per il trasporto multimodale

• Numerical Modeling (Italian)
  Il problema del pendolo

• Numerical Analysis (Italian)
  Metodi iterativi per sistemi lineari e integrazione numerica