## Proposed projects

- Integer partitions and the Arctic Circle theorem

Difficulty level: Introductory

Supervisor: Simon Campese

Tools: Programming can be done in C/C++, Python, R, Matlab/Octave, Wolfram Mathematica, Maple etc., depending on the knowledge of the student.

- Runs in random sequences

Difficulty level:
Introductory/intermediate (some basic knowledge of probability theory is needed)

Supervisor: Simon Campese

Tools:
Programming can be done in C/C++, Python, R, Matlab/Octave, Wolfram Mathematica, Maple etc., depending on the knowledge of the student.

- Benford's law

Difficulty level:
Introductory/intermediate

Supervisor:
Simon Campese

Tools: Programming is best done in R, which can be learned on the spot if you have previous programming experience. Knowledge of (basic) probability theory is needed.

- Playing with Brownian motion paths
Level: Advanced/Research.

Supervision: Ivan Nourdin

Prerequisites: Stochastic calculus

- Gaussian and Poissonian approximations
Level: Medium.

Supervision: Ivan Nourdin

Prerequisites: Probability 1

- Almost sure central limit theorem
Level: Introductory / Medium.

Supervision: Ivan Nourdin

Prerequisites: Probability 1

- Kissing numbers
Level: Introductory.

Supervision: Guenda Palmirotta, Jean-Marc Schlenker.

Prerequisites: analysis 1,2.

Starting date: Winter semester 2019/2020 or later.

- Construction and visualization of flexible polyhedra
Level: Introductory.

Supervision: Guenda Palmirotta, Jean-Marc Schlenker.

Prerequisites: analysis 1.

Starting date: Winter semester 2019/2020 or later.

- Polygon zipping and volumes
Level: Introductory.

Proposed by Andrew Yarmola, who is now at Princeton University.

- Spectrum of flexible polyhedra
Level: Medium.

Supervision: Guenda Palmirotta, Jean-Marc Schlenker.

Prerequisites: analysis 1,2, linear algebra.

Starting date: Winter semester 2019/2020 or later.

- Construction and visualization of domains of dependence
Level: Advanced.

Supervision: Jean-Marc Schlenker.

Prerequisites: basic notions of algebra and geometry. Available for 6th semester BA students.

Starting date: Winter semester 2019/2020 or later.

- Convex hulls of limits sets of hyperbolic or AdS manifolds
Level: Medium/advanced.

Supervision: Jean-Marc Schlenker, NN.

Prerequisites: basic notions of abstract and linear algebra.

Starting date: Winter semester 2019/2020 or later.

- Smooth Numbers

Difficulty level: EML 2 (especially for students in their 3rd semester).

Supervision: Luca Notarnicola.

Starting date: Winter semester 2019/2020 or later.