My fundamental research focuses on symmetries (e.g. invariants, tensor rank) and geometry (e.g. singularity, normality, identifiability) of algebraic varieties related to tensors. These include secant varieties, Hilbert schemes of points, (pre)homogeneous spaces and compactifications of matrix spaces.

I am also interested to more application-driven problems, with a focus on algebraic varieties and symmetries arising in quantum life sciences (e.g quantum states in Quantum Information, excited states in Quantum Physics/Chemistry). Recently,  I have been getting interested into interactions between Algebraic Geometry and MultiPersistent Homology (MPH), specifically on how to deduce persistence invariants from algebraic varieties. 

Since my time at MPI-CBG, I have also been getting hand on analysing real data, specifically via tensor decomposition methods or a combination of signatures-ML methods. 

1. "Schubert compactifications of matrix pencils"
   with F. Gesmundo and H. Keneshlou
   preprint (2026)
   arXiv [math.AG]

2. "On the coupled cluster doubles truncation varieties of four electrons"
   with F. Faulstich, E. Neuhaus and I. Portakal
   preprint (2026)
   arXiv [math.AG, physics.chem-ph]

3. "Some Classical Invariants, from Harmonic Quadruples to Triangle Groups"
   with Giorgio Ottaviani
   preprint (2026)
   arXiv [math.AG]

4. "The GameTheory package for Macaulay2"
   with E. Connelly, Z. He, G. Maletto, E. Neuhaus, I. Portakal, H. Tillmann-Morris, C. Zhao
   preprint (2025)
   arXiv [math.AG]

5. "Discrete signature tensors for persistence landscapes"
   with H. Harrington and D. Tolosa
   preprint (2025)
   arXiv [math.AT] 

6. "Secant varieties of generalised Grassmannians"
   preprint (2024)
   arXiv [math.AG]

7. "Identifiability and singular locus of secant varieties to spinor varieties"
   Communications in Contemporary Mathematics 28(9) (2026)
   journal | arXiv [math.AG] 

8. "Equivariant Euler characteristics on permutohedral varieties"
   with H. Keneshlou and M. Michałek
   Lefschetz Properties: Current and New Directions, Springer INdAM Series 59, pp. 129–154 (2024) 
   journal | arXiv [math.AG]

9. "Identifiability and singular locus of secant varieties to Grassmannians"
   with R. Staffolani
   Collectanea Mathematica 76, pp. 227–249 (2025)
   journal | arXiv [math.AG]

10. "Graph States and the Variety of Principal Minors"
    with F. Holweck
    Annali di Matematica Pura ed Applicata 203, pp. 273–295 (2024)
    journal | arXiv [math.AG, quant-ph]