Currently, I am working on applications of formal methods in computer science and mathematics, “proof mining” the constructive content of results in algebra, and studying differential algebraic geometry using tools from mathematical logic.

2017 Research Statement


  • Explicit polynomial bounds on prime ideals in polynomial rings over fields (with Henry Towsner). In preparation, 2018.
  • Proof mining and effective bounds in differential polynomial rings (with Henry Towsner). arXiv preprint arXiv:1609.07509, 2016. Under review.
  • New examples (and counterexamples) of complete finite-rank differential varieties. Communications in Algebra, 45(7): 3137-3149, 2017. arXiv
  • On linear dependence over complete differential algebraic varieties (with James Freitag and Omar Leon Sanchez). Communications in Algebra, 44(6): 2645-2669, 2016. arXiv
  • Completeness of finite-rank differential varieties. PhD thesis, University of Illinois at Chicago, 2013.