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| Jason Lotay | |
|---|---|
| Name | Jason Lotay |
| Fields | Mathematics |
Jason Lotay is a mathematician specializing in differential geometry, geometric analysis, and gauge theory, with contributions connecting calibrated geometry, special holonomy, and geometric flows. His work spans analysis on manifolds, singularity formation in geometric evolution equations, and applications to moduli problems in differential topology. Lotay has held positions at leading universities and research institutes and collaborated with researchers working on calibrated submanifolds, exceptional holonomy, and mirror symmetry.
Lotay was educated in the United Kingdom, undertaking undergraduate studies that prepared him for research in geometric analysis and differential topology at leading institutions. He completed doctoral studies under the supervision of a prominent geometer, developing expertise in Riemannian geometry, spin geometry, and elliptic partial differential equations. During his graduate training he interacted with mathematicians associated with the study of special holonomy, including groups focused on Calabi–Yau manifold, G2 manifold, and Spin(7) manifold geometry, and engaged with seminars connected to research centers such as the Cambridge University geometry group and the Imperial College London analysis group.
Lotay's early postdoctoral appointments took place at research hubs active in geometric analysis and gauge theory, where he collaborated with experts on calibrated submanifolds, mean curvature flow, and instanton moduli. His career trajectory includes positions that linked British and international mathematical communities, involving institutes such as the Mathematical Sciences Research Institute and research networks around the European Mathematical Society. Lotay has organized and co-organized workshops bringing together researchers in fields including symplectic topology, complex geometry, and low-dimensional topology, fostering interactions between specialists in Donaldson–Thomas theory, Floer homology, and exceptional holonomy.
Throughout his career Lotay has contributed to collaborative projects with researchers working on problems related to singularities in geometric flows, compactness for calibrated cycles, and gluing constructions for special holonomy manifolds. He has engaged with techniques from elliptic operator theory, nonlinear partial differential equations, and index theory, drawing connections to topics studied by groups at institutions such as Princeton University, University of Oxford, and Harvard University.
Lotay has produced results on the analysis and topology of calibrated submanifolds in manifolds with exceptional holonomy, addressing existence, stability, and deformation theory for associative and coassociative submanifolds in G2 manifolds and Cayley submanifolds in Spin(7) manifolds. He contributed to gluing constructions for special submanifolds, building on techniques developed in the study of Donaldson–Uhlenbeck compactness and Taubes's gluing methods, and advanced understanding of unobstructed deformation spaces via analytic estimates related to the Atiyah–Singer index theorem.
In geometric flows, Lotay established results concerning the evolution and singularity formation of calibrated and Lagrangian submanifolds under mean curvature flow and related flows, interacting with work on Huisken's monotonicity formula, White's regularity theorem, and flow techniques used in the study of Ricci flow singularities. He has also studied higher-dimensional gauge theory, including aspects of instanton moduli on manifolds with special holonomy, drawing links to ongoing research in Seiberg–Witten theory and Chern–Simons theory.
Lotay's work includes applications to moduli problems and enumerative invariants inspired by Donaldson–Thomas theory and mirror symmetry, connecting analytic moduli spaces of calibrated cycles to algebraic and symplectic invariants studied in the context of Kontsevich's homological mirror symmetry program. His collaborations have produced constructions of examples of manifolds with exceptional holonomy, building on methods from the study of K3 surface degenerations and gluing frameworks used in the construction of compact G2 manifolds.
Lotay has been recognized by fellowships and invitations to prominent conferences and workshops in differential geometry, geometric analysis, and mathematical physics. He has held competitive research fellowships and visiting positions at institutions known for geometry and topology, receiving invitations to present at meetings associated with societies such as the London Mathematical Society and the American Mathematical Society. His contributions have been acknowledged via prizes and research grants from national research councils and foundations supporting work in pure mathematics.
In academic appointments Lotay has taught courses in differential geometry, geometric analysis, and partial differential equations, supervising graduate students and postdoctoral researchers who have continued work on calibrated geometry, geometric flows, and special holonomy. He has mentored students in dissertation projects connected to deformation theory for calibrated submanifolds, analytical aspects of mean curvature flow, and constructions in higher-dimensional gauge theory, promoting collaboration with researchers in geometry groups at universities including University of Cambridge, Imperial College London, and University of Oxford.
Lotay has also contributed to community-building activities such as organizing lecture series, graduate training programs, and summer schools that connect specialists in symplectic geometry, complex algebraic geometry, and topological quantum field theory to early-career researchers.
- Lotay, J.; coauthors. Works on associative and coassociative submanifolds in G2 manifolds, including analytic and gluing results addressing deformation and compactness phenomena. - Lotay, J.; coauthors. Papers on mean curvature flow for calibrated and Lagrangian submanifolds, studying singularities and long-time behaviour with links to Huisken's monotonicity formula and regularity theory. - Lotay, J.; coauthors. Articles on constructions of manifolds with exceptional holonomy and instanton moduli problems on G2 manifolds and Spin(7) manifolds, connecting to Donaldson–Thomas theory and enumerative geometry.