rof. Nageswari Shanmugalingam is a distinguished research professor (STEMM) in mathematical sciences at the University of Cincinnati, Ohio. She obtained her PhD in mathematics in 1999 from the University of Michigan, Ann Arbor. Her research forms part of the foundation of the emergent field of analysis in metric measure spaces, and her current research interests include nonlinear potential theory, Dirichlet and Neumann boundary value problems in non-smooth setting, and non-local energies, with applications in geometry and quasi-symmetric mappings in non-smooth spaces, including fractals. She has more than 100 research publications in highly ranked mathematical research journals, and has coauthored a book (Cambridge University Press, 2015) on Newton-Sobolev mappings between metric spaces. She also has an extensive mathematical research network both in the U.S. and abroad. Her current research interests include the exploration of how Gromov hyperbolic geometry impacts the behavior of harmonic functions and how the dissipation of heat behaves.
In addition to conducting research in mathematics, Prof. Shanmugalingam is an educator, teaching courses at the undergraduate and graduate levels at the University of Cincinnati. She has also supervised the PhD research of six students and is currently supervising the dissertation research of three other students. She has also been a mentor to postdoctoral scholars.
The development of analysis in non-smooth spaces was motivated by the need to understand how quasi-symmetric classes of regular metric measure spaces share analytic behaviors. This development highlighted the crucial role played by geometric objects called “uniform domains”. On the other hand, recent developments in geometric group theory and fractal analysis indicate a need for discrete analogs of uniform domains. Prof. Shanmugalingam’s Fulbright-Nehru project is developing such analogs in collaboration with Prof. S. Ponnusamy at IIT Madras. The project is also introducing the field of non-smooth analysis to students by conducting a course on analysis in metric spaces.