John Schotland, the Zhao and Ji Professor in Mathematics at Yale University visited RPI on April 7 and 8, 2026 as this year’s honorary Class of ’27 lecturer. His opening colloquium on “Nonlocal PDEs and Quantum Optics” gave a general overview of a novel formulation of the equations of quantum electrodynamics for light interacting with excitable atoms as a system of nonlocal partial differential equations. The nonlocality arises from the second quantization of the photons representing light, which takes a simple form in Fourier space but implies a nonlocal coupling of the light-matter system in physical space. In a second presentation on “Inverse Problems in Quantum Optics,” Dr. Schotland used this nonlocal quantum framework to explore how measurements of light scattering from nanoscale matter could reveal the spatial arrangement of the atoms. This falls within the general framework of “inverse problems” of radiation through matter, a discipline to which Dr. Schotland has been an innovative contributor over his career and in which RPI had hosted an internationally prominent center. Application of inverse problem techniques to the quantum realm naturally brings a greater level of mathematical challenge due to the complexity of the equations of quantum electrodynamics and involves new phenomena such as the role of entanglement between photons.
Dr. Schotland’s two lectures revealed to our faculty and graduate students the rich opportunities presented to mathematicians by the questions raised in an ongoing revolution in quantum devices and materials beyond quantum computing. In addition to the presentations and research meetings, Dr. Schotland shared frank career and scientific wisdom with junior faculty and PhD students over lunch and dinner. The Class of ’27 lecture series is made possible by a generous endowment of mathematics majors from the Class of 1927 in honor of the first chair of the Mathematical Sciences department, Edwin Brown Allen.
