  From the electrical resistivity and ac susceptibility measurements down to
$T$ = 40 mK, a rich temperature-field phase diagram has been constructed for
the geometrically frustrated heavy-fermion compound CePdAl. In the limit of
zero temperature, the field-induced suppression of the antiferromagnetism in
this compound results in a sequence of phase transitions/corssovers, rather
than a single critical point, in a critical region of field 3$-$5 T. In the
lowest temperature region, a power-law description of the temperature-dependent
resistivity yields $A$$\cdot$$T^n$ with $n$$>$2 for all applied fields.
However, a quadratic-in-temperature resistivity term can be extracted when
assuming an additional electron scattering channel from magnon-like
excitations, with $A$ diverging upon approaching the critical regime. Our
observations suggest CePdAl to be a new playground for exotic physics arising
from the competition between Kondo screening and geometrical frustration.
