SEMINAR: Random Patterns and Equilibrium: From Geometry to Dynamics

Abstract: Random objects often exhibit strikingly regular patterns. In this lecture, I will explain how geometric structures naturally give rise to probabilistic models and how, in turn, randomness reveals hidden equilibrium phenomena. We begin with classical questions about the zeros of random polynomials and their natural extensions in complex geometry, where large systems of random equations produce remarkably stable and predictable patterns. As the complexity of these systems grows, their zeros organize themselves in a highly regular way, equidistributing toward natural equilibrium measures arising from potential theory and dynamical systems. I will also describe recent work on the topology of random real algebraic curves, where probabilistic methods help us understand the typical shape and complexity of geometric objects defined by random equations. 

Bio:  Dr. Turgay Bayraktar is a Professor of Mathematics at Sabancı University. He received his B.Sc. and M.Sc. degrees in Mathematics from Middle East Technical University (METU) and his Ph.D. from Indiana University, Bloomington in 2012. His research interests include several complex variables, complex geometry and holomorphic dynamics. His work has been recognized with several awards, including the Science Academy BAGEP Award (2019), the METU Mustafa N. Parlar Foundation Research Incentive Award (2019), the TÜBA-GEBİP Outstanding Young Scientist Award (2019), and the Mathematics Foundation of Turkey Gündüz İkeda Research Award (2019). He served as the Tosun Terzioğlu Chair of Mathematics at Sabancı University from 2022 to 2026.