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Explore how stochastic modeling and analysis provide insights into critical medical questions through this 53-minute conference talk by Sean Lawley from the University of Utah at the Santa Fe Institute. Examine two compelling medical problems where probability theory offers valuable solutions: ovarian tissue cryopreservation as a potential method for delaying or eliminating menopause in healthy women, and medication nonadherence challenges including optimal responses to missed doses and designing robust dosing regimens. Discover how mathematical stochastic theory illuminates these complex medical scenarios while uncovering new mathematical questions that emerge from this interdisciplinary investigation. Learn about collaborative research involving experts from the University of Colorado School of Medicine, Yale University, and Yale School of Medicine that bridges the gap between advanced mathematics and practical medical applications.