Dr. Mohan Swaminathan explores symplectic topology — the geometry that lies between the rigid and the flexible. His research clarifies when and how geometric shapes can be “broken,” “smoothed,” or “counted,” strengthening mathematical foundations that underpin modern geometry and physics.

Dr. Swaminathan develops new tools in enumerative geometry, tackling long-standing problems in the field. His work includes groundbreaking approaches to Gopakumar–Vafa invariants (counting surfaces in six-dimensional spaces), global Kuranishi charts (simplifying foundational machinery), and smoothing of stable maps, all published in leading Mathematics journals. His work bridges abstract mathematical theory with applications in modern physics, establishing new foundations for understanding geometric structures that emerge across scientific disciplines.

Dr. Swaminathan returns from Stanford University and Princeton University, representing geometric training at the highest international level. At the Tata Institute of Fundamental Research (TIFR) in Mumbai, he is developing new mathematical tools while mentoring the next generation to think boldly across traditional boundaries in mathematics.

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