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Using the Hubble UltraViolet Ultra Deep Field (UVUDF), I investigate the star formation in galaxies at the peak of the cosmic star formation history (around redshift of 2) by using the ultraviolet (UV) light as a tracer for star formation. Particularly, I measure the UV luminosity function (LF) to probe the volume-averaged star formation properties of galaxies at these redshifts. The UVUDF allows for a direct measurement of the faint end slope of the UV LF. This redshift range also provides a unique opportunity to directly compare UV to the "gold standard" of star formation indicators, namely the H-alpha nebular emission line. A joint analysis of the UV and H-alpha LFs suggests that, on average, the star formation histories in low mass galaxies (~10^9 Msol) are more bursty compared to their higher mass counterparts at these redshifts.
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