In this thesis I investigate galaxy evolution by measuring the luminosity functions of galaxies across a wide range in redshift. I measure the abundances of high redshift galaxies in deep HST imaging of the GOODS-North field from the CANDELS survey. I follow this evolution to lower redshift by measuring the luminosity functions of galaxies in ground-based imaging of the XMM-LSS field from the VIDEO survey with optical data from the CFHTLS. First, at high-redshift, I identify 22 candidate z ≈ 7 and 6 candidate z ≈ 8 − 9 galaxies. By comparing the number of candidate galaxies with those found in the GOODS-South field, I determine that cosmic variance is not the dominant source of uncertainty on the number counts. I constrain the Schechter parameters for the UV luminosity function at z ≈ 7 and z ≈ 8 − 9, finding evidence for evolution in the number density of high redshift galaxies. Next, I present the K_s-band luminosity functions in the 1 degree² and 4.5 degree² overlaps between the VIDEO-XMM field and the CFHTLS-D1 and CFHTLS-W1 fields. I measure the luminosity functions with the 1/V_max method over the range 0.2 < z < 3 in VIDEO-CFHTLS-D1, and over the range 0.2 < z < 1.5 in the shallower VIDEO-CFHTLS-W1 field. I find the evolution of these luminosity functions is best described by luminosity dependent density evolution, where the characteristic magnitude has dimmed at a constant rate since z = 3, while the density has increased since z = 3, first rapidly from z = 3 to z ≈ 1.5 and then more slowly from z ≈ 1.5 to z = 0.2. I measure a significant upturn at the faint end of the luminosity function at low redshift. Finally, I compare the VIDEO-CFHTLS-D1 and VIDEO-CFHTLS-W1 luminosity functions with predicted K-band luminosity functions from the Horizon-AGN simulation. I find both an over-prediction in the numbers of faint galaxies and an under-prediction in the numbers of bright galaxies, implying that the feedback from supernovae is insufficient while the feedback from AGN is over-sufficient.

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White dwarfs are among the most common objects in the stellar halo; however, due to their low luminosity and low number density compared to the stars in the discs of the Milky Way, they are scarce in the observable volume. Hence, they are still poorly understood one hundred years after their discovery as relatively few have been observed. They are crucial to the understanding of several fundamental properties of the Galaxy – the geometry, kinematics and star formation history, as well as to the study of the end-stage of stellar evolution for low- and intermediate-mass stars. White dwarfs were traditionally identified by their ultraviolet (UV) excess, however, if they have cooled for a long time, they become so faint in that part of the spectrum that they cannot be seen by the most sensitive modern detectors. Proper motion was then used as a means to identify white dwarf candidates, due to their relatively large space motions compared to other objects with the same colour. The use of proper motion as a selection criterion has proven effective and has yielded large samples of candidates with the SuperCOSMOS Sky Survey and Sloan Digital Sky Survey. In this work I will further increase the sample size with the Panchromatic Synoptic Telescope And Rapid Response System 1 (Pan–STARRS1). To construct luminosity functions for the study of the local white dwarfs, I require a density estimator that is generalised for a proper motion-limited sample. My simulations show that past works have underestimated the density when the tangential velocity was assumed to be a constant intrinsic parameter of an object. The intrinsically faint objects which are close to the upper proper motion limits of the surveys are most severely affected because of the poor approximation of a fixed tangential velocity. The survey volume is maximised by considering the small/intermediate scale variations in the observation properties at different epochs. This type of volume maximisation has not been conducted before because previous surveys did not have multi-epoch data over a footprint area of this size. The tessellation of the 3π Steradian Survey footprint is so complex that the variations are strong functions of position. I continue to demonstrate how a combination of a galactic model and the photometric limits as a function of position can give a good estimate of the completeness limits at different colour and different line-of-sight directions. Finally, I compare the derived white dwarf luminosity function with previous observational and theoretical work. The effect of interstellar reddening on the luminosity functions is also investigated.

With energy outputs >~10^51 erg in 0.1-1000 seconds, Gamma-ray Bursts (GRBs) are the most powerful events yet observed in the Universe. As such they are potential probes of the very early Universe, back to the era of re-ionisation and the first stars, but at the same time they have been observed to span a wide range in luminosity and redshift from the relatively local Universe (z~0.0085) out to z~6.29. GRBs divide into two classes based primarily on their duration as measured by T90 (the time taken to observe 90% of the total burst fluence). Long bursts (L-GRBs) have T90>~2 seconds, and shorts (S-GRBs) T90<~2 seconds. Though much has been learned regarding long duration GRBs since the first afterglow discovery in 1997 (including their likely association with massive core collapse supernovae), much remains unknown regarding short duration GRBs. In this work, after a brief historical introduction and review, we present analyses of the angular cross-correlation on the sky of short GRBs from the BATSE catalogue with galaxies in the local Universe sampled from the PSCz Redshift Survey and the Third Reference Catalogue of Bright Galaxies (RC3). In particular we show that 20%+/-8% (1 sigma) of all BATSE short duration bursts (localised to 10 degrees or better) show correlation with galaxy samples (morphological T-type<=4) within ~112 Mpc. Our statistics thus provide evidence that a substantial fraction of BATSE short GRBs show a tendency to be associated with large scale structure on the sky traced by a variety of galaxy types. Short GRBs are believed to be produced in the final merger of compact object (neutron star-neutron star or neutron star-black hole) binaries, though other possible progenitors are known to exist. The short initial spike of a giant flare from a Soft Gamma Repeater (SGR) such as the December 27th 2004 event from SGR1806-20 would have been detectable by BATSE as a short GRB if it occurred in a galaxy within ~30-50 Mpc (assuming a distance to SGR1806-20 of 15 kpc). Using the observed luminosities and rates of Galactic SGR giant flares, as well as theoretical predictions for the rate of binary mergers, we investigate the ability of plausible Luminosity Functions (LF), singly and in combination, to reproduce our observed correlations and a cosmological S-GRB population. We find the correlations are best explained by a separate population of lower luminosity S-GRBs, with properties consistent with them being due to giant flares from extra-galactic SGRs. Overall predicted number counts are a good fit to the observed BATSE number counts, and furthermore, the wider redshift distribution is consistent with the early Swift S-GRB redshift distribution. The three closest GRBs which have been observed to date were all long duration bursts, and we have therefore also searched for cross-correlation signals between the BATSE long GRBs and local galaxies. The three nearby bursts shared several similar properties such as being under-luminous, spectrally soft and of low variability. We have therefore also investigated a subset of L-GRBs with light curve properties similar to these known nearby bursts. The whole sample is found to exhibit a correlation level consistent with zero (1 sigma upper limit=10%, equivalent to 144 bursts) out to a radius of ~155 Mpc, but a spectrally soft, low observed fluence and low variability subset shows a correlation level of 28%+/-16% (=50+/-28 bursts) within 155 Mpc. These results are consistent with low-luminosity, low-variability bursts being a separate sub-class of L-GRBs which may be much more prevalent in the local Universe than their high-luminosity, cosmologically distant counterparts. To investigate this further, we once again examined plausible luminosity functions for single and dual high and low luminosity populations, based on observed intrinsic rates from the literature. The local population was once again found only to be produced to a sufficient level (while maintaining consistency with the observed overall number counts) by a separate low luminosity population with intrinsic rates several hundred times greater than their cosmological counterparts. Constraining the models via the Swift overall redshift distribution instead of threshold-adjusted BATSE number counts showed that the dual LF models were able to produce excellent fits to the entire redshift distribution while adequately reproducing a local population. Finally, suggestions are made as to the direction future work may follow in order to build on these initial investigations, as well as to how observations with future missions and detectors such as Fermi (formerly GLAST), Advanced LIGO and LOFAR may shed further light on nearby GRBs.