  Populating the exoplanet mass-radius diagram in order to identify the
underlying relationship that governs planet composition is driving an
interdisciplinary effort within the exoplanet community. The discovery of hot
super-Earths - a high temperature, short-period subset of the super-Earth
planet population - has presented many unresolved questions concerning the
formation, evolution, and composition of rocky planets. We report the discovery
of a transiting, ultra-short period hot super-Earth orbiting TOI-1075 (TIC
351601843), a nearby ($d$ = 61.4 pc) late K-/early M-dwarf star, using data
from the Transiting Exoplanet Survey Satellite (TESS). The newly discovered
planet has a radius of $1.791^{+0.116}_{-0.081}$ $R_{\oplus}$, and an orbital
period of 0.605 days (14.5 hours). We precisely measure the planet mass to be
$9.95^{+1.36}_{-1.30}$ $M_{\oplus}$ using radial velocity measurements obtained
with the Planet Finder Spectrograph (PFS), mounted on the Magellan II
telescope. Our radial velocity data also show a long-term trend, suggesting an
additional planet in the system. While TOI-1075 b is expected to have a
substantial H/He atmosphere given its size relative to the radius gap, its high
density ($9.32^{+2.05}_{-1.85}$ $\rm{g/cm^3}$) is likely inconsistent with this
possibility. We explore TOI-1075 b's location relative to the M-dwarf radius
valley, evaluate the planet's prospects for atmospheric characterization, and
discuss potential planet formation mechanisms. Studying the TOI-1075 system in
the broader context of ultra-short period planetary systems is necessary for
testing planet formation and evolution theories, density enhancing mechanisms,
and for future atmospheric and surface characterization studies via emission
spectroscopy with JWST.
