Levon Nurbekyan: No-collision transportation maps

I will present a new class of transportation maps inspired by the no-collision property observed in optimal transport. These maps are designed to move mass without overlaps, capturing some of the geometric structure of optimal transportation maps while remaining computationally lighter. I will present the main ideas behind their construction and discuss theoretical aspects such as existence and regularity. I will also examine the relationship between no-collision and optimal transportation maps and discuss some manifold learning applications where no-collision maps perform at the level of, or better than, optimal transportation maps at a lower computational cost. I will conclude by highlighting some of the challenges that remain for broader adoption and outlining possible directions for future research.

Bio: Levon Nurbekyan is an Assistant Professor in the Department of Mathematics at Emory University. He previously held postdoctoral and visiting positions at UCLA, McGill, KAUST, the National Academy of Sciences of Armenia, and the Technical University of Lisbon. Nurbekyan obtained his Ph.D. in Mathematics from the Technical University of Lisbon through the UT Austin—Portugal CoLab program. His research interests include calculus of variations, optimal control, game theory, artificial intelligence and machine learning, optimal transportation theory, shape optimization problems, and dynamical systems.