WE PROPOSE TO USE KEPLER K2 MISSION OBSERVATIONS OF ~1800 SUPERMASSIVE BLACK HOLES AT THE CENTERS OF GALAXIES (ACTIVE GALACTIC NUCLEI; AGN) TO TEST MODELS FOR ACCRETION PHYSICS TO STUDY THE RELATIONSHIP BETWEEN VARIABILITY AND OTHER AGN PROPERTIES SUCH AS ACCRETION RATE AND TO GUIDE METHODS FOR DETECTING AND CLASSIFYING AGN IN FUTURE TIME-DOMAIN SURVEYS. AGN EXHIBIT OPTICAL BRIGHTNESS FLUCTUATIONS ON TIMESCALES FROM BELOW AN HOUR UP TO MANY YEARS. THESE FLUCTUATIONS ARE DETERMINED BY THE PHYSICS OF ACCRETION OF MATTER ONTO BLACK HOLES FROM THEIR GALACTIC ENVIRONMENT. BY OBSERVING VARIABILITY ON TIMESCALES DOWN TO BELOW AN HOUR KEPLER PROBES THE ACCRETION REGION ON LENGTH SCALES THAT ARE TOO SMALL TO BE DIRECTLY IMAGED USING CONVENTIONAL TELESCOPES. THESE DATA ALLOW US TO TEST COMPETING MODELS FOR ACCRETION PHYSICS THAT MAKE DIFFERENT PREDICTIONS FOR THE STATISTICS OF VARIABILITY. OUR PREVIOUS WORK PROVIDES STRONG EVIDENCE THAT MODELS OF AGN VARIABILITY THAT WORK ON LONG TIMESCALE DATA ARE NOT ADEQUATE TO DESCRIBE THE FULL RANGE OF FLUCTUATION TIMESCALES PROBED BY KEPLER. WE WILL ANALYZE THE LIGHT CURVES OF ~1800 AGN THAT HAVE BEEN MONITORED BY KEPLER DURING RECENT AND ONGOING K2 CAMPAIGNS. THESE OBJECTS SPAN A LARGE RANGE OF LUMINOSITY AND AGN TYPE THUS ALLOWING STUDY OF THE RELATIONSHIP BETWEEN VARIABILITY AND OTHER PHYSICAL PROPERTIES. WE WILL CHARACTERIZE THE STATISTICS OF AGN VARIABILITY USING STATE-OF-THE-ART METHODS OF TIME SERIES ANALYSIS THAT ARE APPROPRIATE FOR QUANTIFYING THE STOCHASTIC BEHAVIOR OF AGN. THIS ANALYSIS BUILDS ON OUR PREVIOUS WORK IN WHICH WE DEVELOPED AND TESTED NEW ANALYSIS SOFTWARE THAT EXTRACTS THE FULL INFORMATION CONTENT OF THESE LIGHT CURVES AND WILL ENABLE SEVERAL KEY OUTCOMES: (1) MEASUREMENT OF THE RELATIONSHIP BETWEEN TYPES OF AGN AND THEIR VARIABILITY. (2) TESTS FOR DEPENDENCE OF VARIABILITY ON ACCRETION RATE. (3) INVESTIGATION OF CHANGES IN VARIABILITY BEHAVIOR THAT POINT TO CHANGES IN THE MODE OF ACCRETION. (4) CORRELATIONS BETWEEN THE STOCHASTIC MODEL PARAMETERS AND PHYSICAL PARAMETERS WILL PROVIDE NEW METHODS FOR CLASSIFICATION OF AGN FROM THEIR VARIABILITY AND AID IN IDENTIFICATION OF AGN FROM PHOTOMETRIC SURVEYS. (5) RESULTS OF THIS EMPIRICAL STUDY WILL SERVE AS A GUIDE TO THEORISTS WHO STUDY THE COMPLEX ASTROPHYSICS OF ACCRETION. (6) SENSITIVITY ANALYSIS OF THESE STATISTICS TO CADENCE WILL ALLOW US TO MAKE FORECASTS FOR DETECTION AND CLASSIFICATION OF AGN FROM FUTURE SURVEYS SUCH AS LSST. RESULTS OF THIS RESEARCH WILL INCLUDE NEW CONSTRAINTS ON MODELS OF ACCRETION PHYSICS MORE POWERFUL METHODS FOR CLASSIFYING AGN BY THEIR VARIABILITY AND FORECASTS THAT GUIDE DESIGN OF FUTURE TIME-DOMAIN SURVEYS OF AGN. PRODUCTS OF THIS PROGRAM WILL INCLUDE A CATALOG OF PRECISION LIGHT CURVES OF AGN VARIABILITY MODEL PARAMETERS FOR EVERY LIGHT CURVE AND A SOFTWARE PACKAGE FOR TIME SERIES STATISTICAL ANALYSIS. THUS THE PROPOSED RESEARCH DIRECTLY ADDRESSES A KEY NASA GOAL IN ASTROPHYSICS IN THE AREA OF COSMIC ORIGINS (UNDERSTANDING THE FORMATION OF BLACK HOLES AND THEIR IMPACT ON GALAXIES). THIS RESEARCH PURSUES SEVERAL SCIENCE THEMES IDENTIFIED BY THE 2010 DECADAL SURVEY: DISCOVERY (OPENING THE TIME DOMAIN); ORIGINS (ORIGIN OF BLACK HOLES); AND FRONTIERS OF KNOWLEDGE (NATURE OF COMPACT OBJECTS). THE RESEARCH TEAM FOR THIS PROJECT COMBINES EXPERTISE IN TIME SERIES ANALYSIS VARIABILITY STUDIES OF AGN STATISTICAL ANALYSIS OF LARGE SURVEYS KEPLER PHOTOMETRY AND MULTI-WAVELENGTH OBSERVATIONS OF QUASARS AND AGN. THIS WORK IS TIMELY BECAUSE OBSERVATIONS FROM THE K2 CAMPAIGNS NOW INCLUDE A LARGE SET OF HIGH-CADENCE LIGHT CURVES WITH VERY HIGH-QUALITY PHOTOMETRY AND WE HAVE FULLY TESTED OUR METHODS AND ANALYSIS SOFTWARE.