• Whitney smooth interpolation theorem for maximal Lagrangian tori in nearly-integrable Hamiltonian systems 
• Stability estimates in KAM theory (also computer assisted) 
• Analytic properties of invariant tori at the break-down threshold 
• Arnold diffusion (general theory for a priori unstable systems; variational estimates on diffusion speeds) 
• Direct proof of convergence of Lindstedt series and direct proof of Kolmogorov's theorem on persistence of invariant tori (via graph theory) 
• Extension of Moser's theory to lower dimensional elliptic tori 
  Existence of invariant tori in physical "sub-models" of the Solar system (computer-assisted) 
• Dissipative KAM theory for the spin-orbit problem 
• Completion and extension of Arnold's project on the existence of invariant tori for the planetary N-body problem 
  One dimensional Schrödinger operators: 
• Spectral theory of quasi-periodic perturbations of periodic Schrödinger operators 
• Aysmptotic estimates on eigenfunctions 
  Infinite dimensional Hamiltonian systems and PDEs: 
• Almost periodic solutions for infinite dimensional systems of interacting particles 
• KAM quasi-periodic solutions for nonlinear wave equations with periodic BC 

Other:

• Invited speaker IMC Seoul 2014 (Section 9: Dynamical Systems and Ordinary Differential Equations)
• Prix 1995 Institut Henri Poincaré (first edition)
• the papers Drift and diffusion in phase space and A direct proof of a theorem by Kolmogorov in Hamiltonian systems have been selected by the AMS for the volume "FEATURED REVIEWS in Math Rev 1995-96. Reviews of Outstanding Recent Books and Papers, American Mathematical Society 1997".
• Director of the local unit ROMA TRE for the "PRIN" project (MURST/MIUR) Variational methods and nonlinear differential equations (1998-1999, 2000-2001, 2002-2003, 2004-2005, 2006-2007) 
  Roma Conference (January 10-14, 2005) 
  Director of the local unit ROMA TRE for the "PRIN" project ( MIUR) Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations"prin2009" (2010-2011)
  • Member of the scientific committee for the conferences (last ten years): 
    Global dynamics in Hamiltonian systems (Girona, Spain, 28 June - 4 July 2015) 
    Dynamics, Topology and Computations (Bedlewo, Poland, June 15 - 20, 2015)
    New Perspectives on the N-body Problem (Banff, Canada, January 13-15, 2013)
    Dynamics, topology and computations (Bedlewo, Poland, June 24 - 30, 2012) 
    Dynamics, topology and computations (Bedlewo, Poland, May 31- June 6, 2009) 
    Hamiltonian Systems - Special Session at the Poitiers AIMS Conference(Poitiers, France, June 25-28, 2006) 
    Dynamics, topology and computations (Bedlewo, Poland, June 4-10, 2006)
  • invited lecturer in about 70 international conferences
  • Director of Graduate Studies of the Doctoral School in Mathematical and Physical Sciences of  Roma Tre
  • The main-belt asteroid 114829 Chierchia - 2003 OC21 (discovered 2003 July 23 by the Campo Imperatore Near Earth Object Survey) has been given his name.