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.
- 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.
- On linear dependence over complete differential algebraic varieties (with James Freitag and Omar Leon Sanchez). Communications in Algebra, 44(6): 2645-2669, 2016.
- Completeness of finite-rank differential varieties. PhD thesis, University of Illinois at Chicago, 2013.