Lemanic Neuroscience Doctoral Program, University of Lausanne
and University of Bologna, Italy
The Sense Innovation and Research Center
Lausanne and Sion, Switzerland
MatTech Lab, The University of Applied Sciences of Western Switzerland (HES-SO Valais)
email: gianluca.giacchi [at] unibo.it
Time-frequency analysis topics, such as Gabor frames, pseudodifferential operators, Fourier Integral Operators and their applications to signal analysis and engineering. Compressed sensing and its applications to inverse problems in Magnetic Resonance Imaging (MRI). Machine Learning applications to inverse problems in MRI.
I was born in Milan, where I studied my Bachelor’s and Master’s degrees in Mathematics at University of Milan (Unimi). I acquired a general background during my bachelor’s period, both in theoretical and applied aspects of mathematics. My master’s degree was focused on modern mathematical analysis, with particular emphasis on harmonic analysis and its multiple branches, such as Fourier and time-frequency analysis. In my master’s thesis, I studied pseudo-differential operators in a time-frequency setting, proving the equivalence between the continuity of Wigner distributions and that of discrete convolution on ultra-modulation spaces. Then, I studied fractional Hermite operators on modulation spaces and the most recent results about the related Cauchy problems in a time-frequency setting. During my first year as a Ph.D. student at University of Bologna (Unibo), I started working both on convex optimisation problems, with respect to their applications to MRI reconstruction, and on symplectic time-frequency analysis.