Education

• Ph.D. in Mathematics, Northwestern University, 2007;
• Laurea in Matematica, Universita’ degli Studi, Milano, 2002;
• M.Sc. in Pure Mathematics, University of East Anglia, 2001.

Research Interests

Aldi's research focuses on mathematical problems inspired by physics, using primarily techniques from differential geometry, algebraic geometry, homological algebra and representation theory. Recent areas of inquiry include quantum computational complexity, arithmetic geometry, generalized differential geometry, cohomology of nilpotent Lie algebras, Hamiltonian quantization of the sigma-model, and categorical foundations of analysis.

Select Publications

• M. Aldi, S. Gharibian, and D. Rudolph, “An unholy trinity: TFNP, polynomial systems, and the quantum satisfiability problem”, Leibniz International Proceedings in Informatics (ITCS 2026), Volume 362.
• M. Aldi, J. Buffkin II, C. Cline, and S. Cox, “Sparse systems of functions and quasi-analytic classes”, Fundamenta Mathematicae,  (2025).
• M. Aldi, A. Butler, J. Gardiner, D. Grandini, M. Lichtenwalner, K. Pan,  “On the Cohomology of Lie Algebras associated with Graphs”,Journal of Pure and Applied Algebra (2025).
• M. Aldi, S. Da Silva, and D. Grandini, “A Note on the Shifted Courant-Nijenhuis Torsion”, Journal of Differential Geometry and its Applications  (2024).
• M. Aldi and S. Bevins, “2-step Nilpotent L-infinity algebras and Hypergraphs”, Journal of Pure and Applied Algebra (2024).
• M. Aldi, S. Da Silva, and D. Grandini, “A Note on the Shifted Courant-Nijenhuis Torsion”, Journal of Differential Geometry and its Applications (2024).
•  M. Aldi and D. Grandini, “Polynomial Structures in Generalized Geometry”, Differential Geometry and its Applications, (2022)
• M. Aldi, N. de Beaudrap, S. Gharibian, S. Saeedi, "On efficiently solvable cases of quantum k-SAT", Comm. Math. Phys. (2021).
• M. Aldi, R. Heluani, “A complex-symplectic mirror pair”, Int. Math. Res. Not. (2018).
• M. Aldi, A. Perunicic, “p-adic Berglund-Huebsch Duality”, Adv. Theor. Math. Phys. 19 (2015).

Professional Appointments

• 2019-present, Associate Professor, VCU Dept. of Mathematics and Applied Mathematics.
• 2012-2019, Assistant Professor, VCU Dept. of Mathematics and Applied Mathematics.
• 2010-2012, NSF-FRG Visiting Assistant Professor, Brandeis University Mathematics Dept. (joint appointment with Physics).
• 2007-2010, Charles B. Morrey Assistant Professor, University of California, Berkeley.