Welcome! I am a mathematician working at the boundaries of computer science, logic, and algebra. As a postdoc in the Logical Systems Lab at Carnegie Mellon University, I apply tools from mathematical logic and computational algebra to cyber-physical systems. In other research, I “proof mine” the constructive content of results in algebra and use model theory to study differential algebraic geometry.
Publications
- Explicit polynomial bounds on prime ideals in polynomial rings over fields (with Henry Towsner). Pacific Journal of Mathematics, 306(2): 721-754, 2020. arXiv
- Proof mining and effective bounds in differential polynomial rings (with Henry Towsner). Advances in Mathematics, 343: 567-623, 2019. arXiv
- 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. UIC Indigo repository
William Simmons 