Master projects

Current projects

Miguel Nuno Pereira Santiago: "Mean-value property for functions on the Heisenberg group"

Ana Catarina Tavares Cirne Valente: "Mathematical modelling of video-game economics"

Antonio Cafualica Mendes: "Motion planning via optimal control"

Simao Andrade Lucas: "Gauss-Bonnet formula for Grushin manifolds"

Image reconstruction. Create a blazing-fast algorithm for reconstruction of images using group theory and diffusion on graphs
Basic requirements: Programming.
Crypto-tracker. Create a tool that would allow to harvest data from a blockchain and analyze some examples.
Basic requirements: Programming and some knowledge of search algorithms.
Stable configurations of elastic networks. Create a tool that would model stable configurations of elastic networks, such as bridges and towers under various external forces.
Basic requirements: Programming, ODEs, differential geometry.

Curvature flows. Study the simplest examples of curvature flows on left-invariant contact structures. Yes, the curvature flows similar to those that were used by Perelman to prove the Poincare conjecture ;) In the case of Lie groups, the flows I have in mind become just ODEs and can be studied using simple methods.
Basic requirements: ODEs, also knowledge of differential geometry is a plus.
Composition of symbols in the H-calculi. Recently R. Yuncken and E. van Erp have developed a general pseudo-differential calculus adapted to subelliptic operators. One of the pieces missing in their theory is a formula for the composition of symbols. The goal is to obtain this formula.
Basic requirements: Differential geometry (Manifolds, vector fields, differential forms, possibly Lie groups).