Levy Flight Search Processes in 2D Geometries | Justin Tzou

Recorded on 06/03/2026 Watch the recording without ads at https://www.nitmb.org/extreme-events-... Title: Levy Flight Search Processes in 2D Geometries Speaker: Justin Tzou This talk was recorded as part of the 'Extreme Events in Biological Function' workshop Workshop Overview: Biological systems often operate with surprising precision across a wide range of spatial and temporal scales, despite influence from noisy or weak signals. From immune cells detecting rare pathogens to animals navigating vast landscapes with minimal cues, these systems appear to leverage--rather than avoid--randomness. Traditional views treat noise as a disruptive force, but emerging research suggests that rare and extreme events can instead be harnessed as constructive elements, providing deterministic-like behavior in otherwise stochastic environments. This workshop aims to bring together experts in applied stochastic processes and biological dynamics to explore the critical yet underdeveloped role of extreme and rare events in enabling reliable biological function. Key biological questions include how neurons transmit signals across crowded synapses, how immune cells detect rare pathogens, and how stochastic extinction events influence the dynamics of cancer or HIV. Beyond physical domains, the workshop will also address rare events in abstract biological spaces such as evolutionary fitness landscapes and decision-making processes. Mathematical approaches central to this work include extreme value theory, large deviation theory, ergodic theory, optimal transport, mean-field theory, and rare event sampling techniques. Through this interdisciplinary lens, the workshop aims to advance both theory and application in understanding how biological systems capitalize on rare events for robust function. The program will include research talks and lightning talks, and will have ample time for participants to foster collaborations. NITMB Overview: The NSF-Simons National Institute for Theory and Mathematics in Biology (NITMB) aims to integrate the disciplines of mathematics and biology in order to transform the practice of biological research and to inspire new mathematical discoveries. NITMB is a partnership between Northwestern University and the University of Chicago. It is funded by the National Science Foundation DMS-2235451 and the Simons Foundations MP-TMPS-00005320. The mission of the NITMB is to create a nationwide collaborative research community that will generate new mathematical results and uncover the “rules of life” through theories, data-informed mathematical models, and computational and statistical tools.