Applied Math Seminar

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Dynamic Doppler Effects Associated with Nonlinear Motion in 4D Spacetime: Mathematics, Physics and Modern Medical Engineering Applications

Speaker: Alex Mahalov, Wilhoit Foundation Distinguished Professor, Arizona State University

Location: Warren Weaver Hall 1302

Date: Friday, February 26, 2027, 2:30 p.m.

Synopsis:

Christian Andreas Doppler was a native of Salzburg and a genius in mathematics and physics. His discovery wields a great influence on the world today. The Doppler effect makes it possible for modern medicine to investigate processes in the human body, and even the theory of an expanding universe is based on Doppler's discovery which was also used in Einstein's work. Gregor Mendel, founder of modern genetics, was Doppler's student.

In this lecture intended for a general audience, I will discuss Doppler's life and scientific contributions. I will also present recent mathematical developments in my group focusing on the nonlinear Doppler effects: dynamic Doppler spectrum induced by nonlinear motion in 3D, relativistic and quantum effects, 4D Frenet-Serret geometry, nonlinear dynamical features and physics-informed AI-ML in 4D Spacetime. Modern medical engineering applications of our work include correction of motion artifacts/features in fMRI Neuroimaging, management of respiratory-induced motion aberrations in imaging of the thoracic region in oncology and the most advanced form of proton beam therapy modulated pencil beam scanning.