Marco Castronovo

Welcome! I am a Ritt Assistant Professor in the Mathematics Department at Columbia University. Here is my CV.

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Research

I am a mathematician working in the field of topology, which aims to establish connections between continuous and discrete phenomena.

The ultimate goal of my research is to understand the structure of symplectic manifolds. To do that, I use ideas from Floer theory, mirror symmetry and cluster algebras. I am also interested in computational aspects of symplectic invariants.

Currently, I am trying to describe generators for the Fukaya category of homogeneous symplectic manifolds.

• Cluster deep loci and mirror symmetry
  with M. Gorsky, J. Simental, D. Speyer
  Submitted
• Curved Fukaya algebras and the Dubrovin spectrum
  Submitted
• Lagrangian cobordism of positroid links
  with J. Asplund, Y. Bae, O. Capovilla-Searle, C. Leverson, A. Wu
  Submitted
• 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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