Ebru Toprak

Ebru Toprak is currently a Gibbs Assistant Professor at Yale University, specializing in the intersection of Spectral Analysis, Partial Differential Equations, and Mathematical Physics. She actively contributes to the academic community by co-organizing Yale's Analysis Seminar with Professors Wilhelm Schlag and Paul Smart.

Her educational foundation includes a PhD from the University of Illinois at Urbana-Champaign, completed under the supervision of Professor M. Burak Erdoğan. This training established her expertise in rigorous mathematical analysis of differential operators and dispersive systems.

Dr. Toprak's research investigates spectral properties of Dirac operators in general-relativistic contexts and decay behavior of solutions to Schrödinger/wave equations with singular potentials. Her work bridges abstract functional analysis with concrete physical applications, particularly in quantum systems near black holes and long-time dynamics of dispersive PDEs. Current projects focus on General Relativistic Dirac operators and dispersive estimates for repulsive Coulomb potentials.

Her publication trajectory reveals consistent contributions to spectral theory and dispersive equations, with increasing emphasis on relativistic quantum models. Key themes include zero-energy resonance analysis, threshold obstruction effects, and mathematical validation of physical phenomena in curved spacetimes.

She has received significant recognition including:

• 2019 AWM Dissertation Prize for outstanding doctoral research
• Editor's pick in Journal of Mathematical Physics (2020) for groundbreaking work on relativistic hydrogen systems

Dr. Toprak maintains active collaborations with leading analysts including Erdoğan, Green, and Kiessling, advancing frontier research in mathematical physics through joint publications and seminar leadership. Her work continues to shape understanding of fundamental operators in quantum gravity contexts.