Applied Mathematics and Statistics Seminar by Jithin George: Two Stories About Complex Analysis in Scientific Computing

Speaker: Jithin George, Center for Nanoscale Materials at Argonne National Laboratory and Northwestern + Argonne Institute for Scientific and Engineering Excellence

 

Title: Two Stories About Complex Analysis in Scientific Computing

 

Abstract: This presentation focuses on two applications of theory from complex analysis for modern scientific computing purposes.

 

The first story is about numerical time integration using complex time steps [1,2]. Traditional numerical time integrators consider only real-valued time steps. By extending time stepping into the complex plane, one can improve both stability and accuracy. We have demonstrated clear computational advantages for complex-valued systems. For quantum systems, such as the Schrödinger equation, we have shown that complex time integrators are uniquely optimal. 

 

The second story is focused on the understanding and interpretation of Electrochemical Impedance Spectroscopy (EIS) data. EIS is a non-invasive technique used to probe the internal behavior of material devices such as batteries and transistors. It is therefore particularly useful for evaluating candidate materials for neuromorphic devices. Standard EIS analysis relies on strong modeling assumptions and can lead to ambiguous or erroneous interpretations. I will talk about my recent framework based on numerical complex analysis that enables more robust interpretation of EIS data [3] without assuming a model. 

 

[1] George, Jithin D., et al. "Explicit complex time integrators for stiff problems." arXiv preprint arXiv:2601.07730 (2026).

[2] George, Jithin D., Samuel Y. Jung, and Niall M. Mangan. "Walking into the complex plane to" order" better time integrators."

[3] George, Jithin D., et al. "Robust interpretation of electrochemical impedance spectra using numerical complex analysis.