Title: The Big 4 of Mathematical Relativity
Abstract: The big 4 conjectures of mathematical relativity started life as intuitive guesses by a number of physicists. After decades of work, mathematicians have been able to translate these intuitions into precise mathematical questions that are amenable to confirmation by proof or refutation by counterexample. These conjectures remain wide open at present and my aim will be to describe what they're about, how they are inter-related, whether they're physically relevant, and how likely it is that we'll see their resolution in the near future.
Title: Searching for a Potentially Missing Population of Lensed z > 6 Quasars
Abstract: The discovery of the first strongly lensed quasar at z > 6 (J0439+1634) is an important step forward in our understanding of the early Universe. After a brief historical overview, I will describe the detection of J0439+1634 and derive its theoretical consequences. We predict that the observed population of z > 6 quasars should contain many mildly magnified sources, possibly with unresolved image separations. Additionally, current selection criteria should have missed a substantial population of lensed z > 6 quasars, due to the contamination of the drop-out photometric bands by lens galaxies. We then estimate the fraction of undetected quasars as a function of the slope beta of the bright end of the quasar luminosity function, finding that they could reach half of the known population. These "phantom quasars" would be misclassified and mixed up with low-z galaxies. The recent claim that the most massive z>6 quasar ever detected might be magnified by a factor 450 is discussed. A consistency check on this detection leads to a lower limit on the bright-end slope of beta>3.7. If confirmed, it is very likely that additional sources in the same SDSS sample are magnified. I conclude by addressing how gravitational lensing can affect the inferred black hole mass distributions at z > 6, possibly having important implications for current growth theories for early quasars.