- Fellowship in 2016 at Harvard University
Dr, Cheung is currently a visitor at the `Cluster algebras and representation theory' program at the Isaac Newton Institute for Mathematical Sciences. During 2017-2021, Mandy was a Benjamin Peirce Fellow in the Department of Mathematics at Harvard University. She was a member at the Institute for Advanced Study at 2016-2017. Mandy received the Croucher Foundation Honorary Fellowship for the year 2016-2018.
Dr. Cheung received her Ph.D. degree (2016) in the Department of Mathematics at University of California, San Diego, M. Phil. degree from the Hong Kong University of Science and Technology, and B.Sc. degree from the Chinese University of Hong Kong.
Dr. Cheung is interested in the interplay between algebraic geometry, and cluster algebras, and mirror duality for the cluster varieties. Cluster algebras were developed by Fomin and Zelevinsky to investigate Lusztig problems on total positivity in algebraic groups. The area has now developed and has links with Poisson geometry, integrable systems, higher Teichmuller spaces, DonaldsonThomas invariants, and the representation theory of quivers. On the other hand, mirror symmetry was motivated from mathematical physics to study dualities between different geometries.
Dr. Cheung has extended the polytope construction in toric geometry to the cluster geometry world. With her collaborators, she has shown the convexity in the tropical work, which she named as the broken line convexity, describing the compactification for cluster varieties. She has also set up the relation between tropical curve counting and quiver moduli.