Marco Castronovo
Assistant Professor of Mathematics
Barnard College, Columbia University
castronovo@math.columbia.edu
Research
I work in the field of Topology, which studies the connections between continuous and discrete phenomena. I focus on symplectic structures as a general framework for the quantization of classical invariants. Currently, I'm interested in developing an open-string version of Schubert calculus.
Articles
-
Cluster deep loci and mirror symmetry
with M. Gorsky, J. Simental, D. Speyer
Communications of the AMS 6 (2026), 1021-1086 -
Curved Fukaya algebras and the Dubrovin spectrum
Accepted in Kyoto Journal of Mathematics -
Lagrangian cobordism of positroid links
with J. Asplund, Y. Bae, O. Capovilla-Searle, C. Leverson, A. Wu
Pacific Journal of Mathematics 332 (2024), no. 1, 1-21 -
Liouville domains from Okounkov bodies
Journal of Topology and Analysis 18 (2026), no. 2, 571-595 -
Exotic Lagrangian tori in Grassmannians
Quantum Topology 14 (2023), no. 1, 65-99 -
Fukaya category of Grassmannians: rectangles
Advances in Mathematics 372 (2020), 107287, 40 pp.
Code
-
DubrovinDynamics
Shows the evolution of eigenvalues in the spectrum of the truncated Dubrovin operator of some Grassmannians, as one deforms the bulk parameters. -
Posetroids
with B. Basson
Generates a list of all positroid strata in a given Grassmannian, together with the partial order on them induced by Zariski closure. It also works for general type A projected Richardson varieties in a given partial flag variety. -
ClusterExplorer
A random walk on the exchange graph of the cluster structure of the top positroid strata. These spaces are believed to support Landau-Ginzburg models for Grassmannians, and the walk allows to study the Laurent polynomials describing the potential in each chart.
Teaching and Mentoring
- Summer 2026: M. Loh, A. Malhotra, E. Zuo (Barnard SRI)
- Spring 2026: MATH 4081GU Introduction to Differentiable Manifolds
- Fall 2025: MATH 1101UN Calculus I
- Summer 2025: B. Basson (Barnard SRI), S. Kesavan (Columbia SRF)