We have observed the nearest ultraluminous infrared galaxy Arp 220 with a 13 month near-infrared observing program using the Canada France Hawaii Telescope to search for obscured supernovae in this extreme star forming environment. This monitoring program was aimed as a feasibility study to determine the practicality of a large scale near-IR LIRG/ULIRG imaging survey. Establishing the supernova rate in these dusty galaxies is an important step toward confirming theorized star formation rates and settling the debate between the dominant energy source in LIRGs: star formation or AGN activity. Both the deduced high star formation rate and far-IR luminosity of Arp 220 suggest an atypically high supernova rate of 1-4 per year, two orders of magnitude greater than that of the Milky Way. We attempt the first direct observation of this rate which to date has been probed primarily through radio measurements of supernovae and remnants. Through a point-spread function matching and image subtraction procedure we find no supernovae outside the galactic nucleus, consistent with the paradigm of a strong nuclear-contained starburst. Image subtraction residuals prevent the discovery of supernovae in the central regions of the galaxy. Using differential photometry we find evidence for a statistically significant brightening in the Arp 220 nucleus with a K-band peak of approximately $\Delta m_K=0.16$ magnitudes. To find the true peak magnitude we use Hubble Space Telescope archival data to subtract off the nuclear background and find an absolute magnitude of $M_K = -22.19 \pm 0.16$ (non-absorbed). This exceeds the luminosity of a typical core collapse supernova by roughly 3.5 magnitudes; rather, the observed variations in nuclear brightness are most likely the signature of an active galactic nucleus embedded in the dusty nuclei of Arp 220 or the superposition of light from several supernovae. This method is not sensitive to the detection of individual supernovae and we cannot rule out the occurrence of any nuclear SNe during the observing period. The brightening event is dimmer in the H and J bands, appearing to be affected by extinction. Interpreting this as a supernova-related event we estimate the extinction in the nuclear regions of Arp 220 to lie between $2.01 \le A_K \le 3.40$ or $17.95 \le A_V \le 30.36$ in the optical, in agreement with several other estimates. Improved resolution is required in order to detect supernovae in the extremely bright nuclear environments of LIRGs. Alternatively, infrared spectroscopy would reveal the telltale spectral features of nuclear supernovae. Spectroscopic observations of the Arp 220 nuclei were conducted using Keck in July 2013 for this very purpose; results are pending. We also explore the hypothesis that type Ia supernovae are produced primarily from young stellar populations. We model elliptical galaxies as two component stellar systems using PEGASE stellar templates: a fixed older underlying population coupled with a younger, less massive population. Varying the age and mass ratio of the young component, we examine its effect on I) the colours and II) the supernova rate of the single underlying population. We explore the effect with redshift and employ both theoretical and observational forms of the type Ia delay-time distribution. We then apply our models to the MENeaCS supernova survey and find that the number and distribution of red sequence SN Ia hosts agrees with theoretical expectations. The lack of evidence for a type Ia rate cutoff argues for a continuous delay-time distribution in support of the double degenerate model as the primary SN Ia progenitor channel. We conclude that it is not possible for all type Ia events in ellipticals to originate from a young frosting of stars. / Graduate / 0606 / jkezwer@uvic.ca