Search for New Heavy Resonances Decaying to $W$, $Z$, or Higgs Bosons and Upgrade of the Compact Muon Solenoid Level-1 Muon Trigger for the High Luminosity Large Hadron Collider

This thesis describes the search for a new heavy boson decaying to a pair of heavy electroweak bosons ($WW$, $WZ$, or $WH$) in the semileptonic final state (electron or muon, missing transverse momentum, and jet), using the data obtained from proton collisions in the Compact Muon Solenoid detector at the Large Hadron Collider. The data used, collected during the second run of the Large Hadron Collider, has integrated luminosities of 35.9 fb$^{-1}$, 41.5fb$^{-1}$, and 59.7fb$^{-1}$ recorded for the years of 2016, 2017, and 2018, respectively. The analysis performed makes use of a novel two-dimensional signal extraction technique performed in the plane of the diboson invariant mass and jet mass, with the search performed in the resonance mass range from 1.0 to 4.5 TeV. Results are obtained in terms of asymptotic exclusion limits, with no significant deviation from Standard Model predictions observed. We also present studies towards a novel muon tracking algorithm for the Level-1 Trigger of the Compact Muon Solenoid detector at the future High Luminosity Large Hadron Collider.