Marco Castronovo

Welcome! I am an Assistant Professor at Barnard College, and an affiliated Junior Faculty in the Mathematics Department at Columbia University.

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Research

• 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
  This shows the evolution of eigenvalues in the spectrum of the truncated Dubrovin operator of some Grassmannians, as one deforms the bulk parameters.
• Posetroids
  This generates a list of all positroid strata in a given Grassmannian, together with the partial order on them induced by Zariski closure.
• ClusterExplorer
  This is 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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