My interests are currently focused on AI problems, and more precisely on Semi-supervised Learning for Image Recognition.
My research in Dynamical Systems is focused on elliptic dynamics, and more precisely on the phenomena related with rigidity (as in K.A.M. theory), phenomena related with the absence of rigidity (as in variants of the Anosov-Katok construction) and the interface between these two worlds.
The main focus of my publications has been the theory of quasi-periodic cocycles in compact Lie groups, which is the discrete-time analogue of quasi-periodic flows in compact Lie groups. I have used and further strengthened the K.A.M.-theoretical tools developed by H. Eliasson and R. Krikorian (among many others), and applied fiberwise Anosov-Katok techniques in the investigation of the transition from quasi-periodic to mildly chaotic behaviour of such systems.
I am also interested in problems in Applied Mathematics, and more specifically in Numerical Analysis for Structural Dynamics, where I am preparing, in collaboration with prof. D.L. Karabalis, a numerical method for the calculation of the seismic response of structures.