Eric Agol Title: New techniques for studying extrasolar planets Abstract: I review several novel approaches to exoplanet detection and characterization, including transit-timing variations (TTV), exoplanet mapping using phase variations and eclipses, and transits of white dwarfs. TTV may be used to characterize multi-planet systems by measuring deviations from periodicity of a transiting planet due to the gravitational pull of companion planets. Many examples of systems with TTV have been found by the Kepler satellite, with eight planet candidates confirmed by this technique. Infrared phase variations measured with Spitzer have been used to characterize the climate of hot Jupiters and to make longitudinal maps, constraining atmospheric circulation models. I will present the first eclipse map of a hot Jupiter based on Spitzer, which may be a taste of what will be done with JWST. Finally, I will look well into the future towards studying Earth-like planets in their habitable zones. Observations of Earth with the EPOXI satellite show that phase variations may be used to make longitudinal maps of habitable planets with continents and oceans, even in the presence of variable cloud cover. Such observations might be carried with future large space-based occulting or coronagraphic telescopes. I will conclude with a more speculative idea on the detection and characterization of habitable planets around white dwarfs