  M-dwarf stars below a certain mass are convective from their cores to their
photospheres. These fully convective objects are extremely numerous, very
magnetically active, and the likely hosts of many exoplanets. Here we study,
for the first time, dynamo action in simulations of stratified, rotating fully
convective M-dwarf stars. Importantly, we use new techniques to capture the
correct full ball geometry down to the center of the star. We find surprising
dynamo states in these systems, with the global-scale mean fields confined
strongly to a single hemisphere, in contrast to prior stellar dynamo solutions.
These hemispheric-dynamo stars are likely to have profoundly different
interactions with their surroundings, with important implications for exoplanet
habitability and stellar spindown.
