This is a proposal for a M2 internship followed by a PhD thesis. The PhD thesis objectives will be twofold. One objective will consist in using the data that CMS will record during Run 3 together with the Run 2 data, and probe for the first time the polarization in diboson (ZZ) VBS events. This analysis will pave the way towards more precise measurements of polarization fractions in VBS events at the HL-LHC and understanding the role of the Higgs boson in the regularization of VBS processes. The other objective will consist in optimizing, on simulated data, the reconstruction of particle showers in the HGCAL at the L1 trigger, and validating it on the real system hardware. Exploratory studies of implementing distributed machine learning techniques (such as deep neural networks) on FPGAs (field-programmable gate array) is also foreseen. The M2 internship subject will be an introduction to one of the two PhD thesis objectives presented above.