**Abstract**

Our research group in Mathematics Department -- UNICAMP focus on the study of intertwined properties of stochastic analysis, geometry and dynamical systems, mainly concerning the theory of continuous semimartingales (e.g. Brownian motion), and more recently including jumps (e.g. Lévy processes). This project, which connects researchers who use common techniques on probability and ergodic theory is centred on the following items: stochastic dynamics on manifolds (bifurcation of Markov processes via $n$-point processes), properties of certain SPDEs, diffusions on foliated spaces, decomposition of stochastic flows (and its applications in dynamics and geometry of associated bundles), coupled systems and equilibrium for cellular automata with memory. The project is guided mainly by the following actions: i) support the orientation of masters and PhDs/researchers; ii) improve further the national and international scientific connections, with a continuous flow of top researchers coming to visit the group, or members of the group going to congresses, visiting collaborators and centres of top reputation in the area. (AU)

Scientific publications
(26)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)