Title of the talk: Mathematics, Modeling, and Insight: From Ideas to Impact

Date, Time & Venue: 19 Dec'25 at 4:30 PM - 5:15 PM on Seminar Room, Dept. of Mathematics

Abstract: Mathematics provides a fundamental language for understanding natural phenomena and for enabling many of today’s advanced technologies, including photonics, nonlinear devices, quantum systems, and machine learning–based computational methods. My research lies at the intersection of applied mathematics, physics, and technology, with an emphasis on developing mathematically grounded models and computational tools for complex wave-based and nonlinear systems.

In this talk, I will present selected contributions from my work on optics and photonics, nonlinear dynamical systems, and the analysis of non-self-adjoint differential operators, highlighting how mathematical structure informs physical understanding and device-level modeling. I will also discuss recent progress in the numerical solution of differential equations using physics-informed neural networks, which combine governing physical laws with data-driven learning to address challenges faced by traditional numerical methods.

The talk will conclude with an outlook on future research directions and the role of mathematics in shaping next-generation scientific and engineering applications.