• Supervised Learning: SVM, Decision Trees, Random Forests;
• Unsupervised Learning: Clustering, PCA;
• Neural Networks: modeling, activation function and regularization methods;
• More advanced NN structures: Siamese Networks, AutoEncoders.

Grade: 110 with honors/110

Title: Oil And Water and Internal Diffusion Limited Aggregation
Supervisor: Lorenzo Taggi

Short description: Oil And Water and Internal Diffusion Limited Aggregation are two randomly interacting particle systems on graphs. We considered, for both, two questions:

• the phase transition with respect to the initial particle density between the two regimes of fixation and activity;
• internal aggregation. Oil And Water has not a complete theory about internal aggregation, hence we analyzed a conjecture and introduced a new simpler model not present in the literature, with the same cluster growth rate as Oil And Water. We also compared the particles distributions on the clusters of the models and analyzed their fluctuations.

Title: Mathematical formalization of the financial market and CRR Model
Supervisor: Gustavo Posta

Short description: Probabilistic description of a financial market, in order to study the CRR and the Black-Scholes model.