  Great strides have been made in recent years in the understanding of the
mechanisms involved in the formation and evolution of planetary systems;
despite this, many observational facts still do not have an explanation. A
great contribution to the study of planetary formation processes comes from the
study of young, low-mass planets, with short orbital periods. In the last
years, the TESS satellite has identified many planets of this kind, and their
characterization is mandatory to understand how they formed and evolved. Within
the framework of the GAPS project, we performed the validation and
characterization of the ultra-short period planet (USPP) TOI-1807b, orbiting
its young host star BD+39 2643 (~300 Myr) in only 13 hours. This is the
youngest USPP discovered so far. Thanks to a joint modeling of the stellar
activity and planetary signals in the TESS light curve and in HARPS-N
radial-velocity measurements, combined with accurate estimation of stellar
parameters, we validated the planetary nature of TOI-1807b and measured its
orbital and physical parameters. By using astrometric, photometric, and
spectroscopic observations we found that BD+39 2643 is a young, active K dwarf
star, member of a 300+/-80 Myr old moving group and that it rotates in
Prot=8.8+/-0.1 days. This star hosts an USPP with an orbital period of only
P_b=0.54937+/-0.00001 d. Thanks to the exquisite photometric and spectroscopic
series, and the accurate information on the stellar activity, we measured both
the radius and the mass of TOI-1807b with high precision, obtaining
R_b=1.37+/-0.09 R_Earth and M_b=2.57+/-0.50 M_Earth. These planet parameters
correspond to a rocky planet with an Earth-like density and no extended H/He
envelope. From the analysis of the age-R_P distribution for planets with well
measured ages, we inferred that TOI-1807b may have already lost a large part of
its atmosphere during its 300 Myr life.
