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, T. Gabrielsen, D. Grandini, J. Harris, and K. Kelley. "Independence Polynomials of 2-step Nilpotent Lie Algebras." Journal of Pure and Applied Algebra, Vol. 230 (2026)
• 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).