U of T Engineering professor Adrian Nachman (ECE) has been elected a 2025 fellow of the Royal Society of Canada (RSC). The RSC’s mission is to advance knowledge, encourage integrated interdisciplinary understanding and address issues that are critical to Canada. Fellowship in the RSC is one of the highest honours a Canadian scholar can achieve.
Nachman is internationally renowned for his breakthroughs in mathematical problems related to medical imaging, some of which had been unsolved for decades. His career is distinguished by a rare combination of fundamental contributions published in top mathematical journals and extensive collaborations with bioengineers to apply his novel ideas to new medical diagnostic technologies.
In medical imaging, the goal is to determine interior structures in the body noninvasively from measurements of acoustic or electromagnetic waves. Waves are modeled as solutions of differential equations that depend on the medium of propagation. This leads to what are known as inverse problems, as their aim is essentially to compute causes from observations of effects. Nachman is known as one of the most original and influential thinkers to have tackled these important mathematical problems.
Nachman has also collaborated with bioengineers and clinical researchers to advance medical imaging technologies. Before joining U of T, he worked with colleagues at the University of Rochester to develop quantitative ultrasound imaging instrumentation for early breast cancer detection. A numerical method developed in this collaboration for simulation of ultrasonic pulses spanning hundreds of wavelengths is now a standard approach in the field. In his research on electric imaging, Nachman invented a method for determining the electric conductivity of tissue from measurements of currents obtained using Magnetic Resonance Imaging by colleagues in biomedical engineering at U of T. The resulting series of joint papers and patent were novel contributions to the area of hybrid inverse problems, which couple two distinct physical responses of tissue to achieve unprecedented high resolution and high contrast images.
As an expert on the mathematics of medical imaging, Nachman was approached by Mitacs to be lead organizer of a Focus Period on the subject. The program he assembled included a major interdisciplinary conference in Toronto and several workshops — on brain imaging, cardiac imaging, numerical procedures, and analytic methods — in Toronto, Vancouver and at the Isaac Newton Institute in Cambridge, UK. In 2013, he gave the Society for Industrial and Applied Mathematics Invited Address at the Joint Mathematics Meetings. In 2014, he was named a Fields Institute Fellow.
“Professor Adrian Nachman’s novel solutions to longstanding inverse problems have enabled key breakthroughs in developing next-generation medical diagnostic imaging methods,” says Christopher Yip, Dean of the Faculty of Applied Science & Engineering.
“On behalf of the faculty, I congratulate him on this prestigious honour.”