معرفی
Marco Castronovo serves as an Assistant Professor in the Mathematics Department at Columbia University, with his office located in Mathematics Hall 614. His academic work bridges continuous and discrete mathematical structures through the lens of symplectic geometry and topology.
His research focuses on Symplectic Topology, particularly exploring symplectic structures as frameworks for quantization of classical invariants. Key interests include:
- Developing open-string versions of Schubert calculus
- Investigating cluster structures in positroid varieties
- Constructing Landau-Ginzburg models for Grassmannians
- Studying Lagrangian cobordisms and exotic tori
- Analyzing connections between Dubrovin spectra and Fukaya algebras
His recent publications reveal a consistent trajectory toward unifying symplectic geometry with combinatorial algebraic structures, particularly through Grassmannian varieties and their mirror symmetric counterparts. The work demonstrates increasing sophistication in connecting Fukaya categories with cluster algebraic frameworks, while maintaining strong ties to quantum topological invariants.
As an academic mentor, Castronovo supervises undergraduate researchers including B. Basson (Barnard Summer Research Institute) and S. Kesavan (Columbia Summer Research Fellowship). He actively contributes to the mathematical community through refereeing and co-organizing the Columbia SGGTC Seminar, demonstrating commitment to both research dissemination and academic service.
His computational work manifests through three significant open-source projects: Posetroids for exploring Zariski closure orders in Grassmannians, DubrovinDynamics for visualizing spectral evolution in truncated Dubrovin operators, and ClusterExplorer for conducting random walks on cluster structures of Grassmannians. These tools have become valuable resources for researchers working at the intersection of symplectic geometry and combinatorics.
