Rate My Professor Ivan Smith

Ivan Smith is Professor of Geometry in the Faculty of Mathematics at the University of Cambridge, affiliated with the Department of Pure Mathematics and Mathematical Statistics (DPMMS) and the Differential Geometry & Topology research group. He serves as a Fellow and College Lecturer at Gonville & Caius College. Smith obtained his BA and D.Phil in Mathematics from the University of Oxford. His research specializes in symplectic topology, a field originating from the study of periodic orbits in mechanical systems and featuring deep connections to theoretical physics. Central to his work is Floer theory and the Fukaya category, which encapsulate counts of solutions to partial differential equations within global invariants governed by non-commutative algebra. This framework underpins homological mirror symmetry, a conjectural bridge between analytic and algebraic geometry aspects, initially anticipated in string theory.

Collaborating with various researchers, Smith has employed Floer theory to develop novel invariants for knots and links, derive universal constraints on billiard trajectories across flat surfaces, prove that symplectic symmetry groups possess infinite complexity, and verify additional cases of mirror symmetry. His impactful contributions have garnered major accolades: the London Mathematical Society Whitehead Prize (2007), the Adams Prize (2013), an invited lecture at the International Congress of Mathematicians (2018), designation as Clay Senior Scholar (2022), and election as Fellow of the Royal Society (2023). Key publications encompass 'Spectral Floer theory and tangential structures' (2026, with N. Porcelli), 'Symplectomorphisms and spherical objects in the conifold smoothing' (2025, with A. Keating), 'Gromov-Witten Invariants in Complex and Morava-Local K-Theories' (2024, with M. Abouzaid and M. McLean), 'Irrationality and monodromy for cubic threefolds' (2023), 'Double bubble plumbings and two-curve flops' (2023, with M. Wemyss), 'Quantitative Heegaard Floer cohomology and the Calabi invariant' (2022, with D. Cristofaro-Gardiner et al.), 'Floer Theory of Higher Rank Quiver 3-folds' (2021), and 'Fukaya categories of surfaces, spherical objects and mapping class groups' (2021, with D. Auroux). Smith organizes workshops like 'Floer theory beyond Floer' (2026) and supervises doctoral students in symplectic and low-dimensional topology.