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High throughput DNA sequencing has transformed the landscape of genomic data and is expected to revolutionize our knowledge of evolution and genomic function. These data are expected to be of particular benefit to the study of recent
evolutionary processes, due to our ability to sequence multiple individuals from closely related species. While much excitement revolves around these emerging data sets, realizing this potential requires developing powerful and efficient inference methods that are capable of extracting insights on recent evolution from genome-wide sequence data. In this talk, I will be presenting some of my work in this area,
which examines what we can learn from complete individual genome sequences on population history and recent natural selection. I will start by describing a study on ancient human population demography in Africa, focusing on one of the deepest population divergence events in human history, dating roughly 130 thousand years ago.
I will then present work I did as part of a large-scale collaborative effort to study the early evolution of dogs using the complete genome sequences of two dogs and three gray wolves. I will show how we were able to settle several longstanding debates revolving around the origins of dogs using these genomes and an innovative computational approach. Lastly, I will introduce a line of research I recently
initiated, focused on studying the evolutionary roles of non coding regulatory elements in the human genome. I will present recently published work on natural selection on human transcription factor binding sites, and ongoing efforts to extend that approach to all functional non coding elements in the genome. The talk will focus on the main findings in these three studies and how they contribute to our understanding of recent evolution. I will highlight the computational challenges involved, and will conclude with a map of the opportunities and challenges we face in the study of evolution in a world of rapidly evolving genomic data sets.

Obtaining correlation functions in quantum impurity models, which are often to describe charge and spin transport through molecules and quantum dots, is a matter of major importance in condensed phase materials science. In particular, in the language of these functions a rigorous mapping exists between bulk strongly correlated electron systems (such as transition metal oxides) and interacting impurities embedded within a non-interacting effective bath, via the "dynamical mean-field theory" (DMFT). The extraction of dynamical properties like correlation functions from the imaginary-time Monte Carlo methods commonly used within DMFT is an ill-posed problem, and reliable results both for transport in molecular electronics and DMFT require real-time methods. Unfortunately, until now such methods have only addressed single-time properties such as state populations and transport, while correlation functions are two-time observables.

We have developed a numerically exact real time quantum Monte Carlo method for computing correlation functions of impurity models in equilibrium and nonequilibrium. We show that with this tool we can reliably resolve the spectral function of weakly and strongly correlated impurities at all frequencies. We go on to consider an impurity in a junction, where we show how the correspondence between the spectral function and the differential conductance breaks down when nonequilibrium effects are taken into account. Finally, a long-standing dispute regarding this model has involved the voltage splitting of the Kondo peak, an effect which was predicted over two decades ago by approximate analytical methods but was never successfully confirmed by reliable numerics. We finally settle this issue by demonstrating that the splitting indeed occurs.