Marco Castronovo

Welcome! I'm a Barnard Assistant Professor in the Mathematics Department at Columbia University. You can find me in office 614 of Mathematics Hall, or contact me at lastname@math.columbia.edu

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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
  Submitted
• 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
  Accepted in Pacific Journal of Mathematics
• Liouville domains from Okounkov bodies
  Accepted in Journal of Topology and Analysis
• 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.

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Teaching

• Summer 2025: B. Basson (Barnard SRI), S. Kesavan (Columbia SRF)
• Fall 2025: MATH1101UN Calculus I
• Spring 2026: MATH4081GU Introduction to Differentiable Manifolds

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Service

• I'm currently refereeing 1 paper
• I co-organize the Columbia SGGTC Seminar