# Marco Castronovo

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

### 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.