My PhD research was in real algebraic geometry / symbolic computation under Dr. Hoon Hong. My dissertation provided an improved degree bound on exactifying multipliers for Descartes’ Rule of Signs and detailed the conditions for optimality of the bound.
- Descartes’ Rule of Signs: the number of positive real roots of a polynomial f is bounded by the number of sign changes in the coefficients of f.
- Exactifying Multipliers: a polynomial g such that the number of positive real roots of f is exactly the number of sign changes in the coefficients of gf.
- Elliptic curves, modular forms, and sums of Hurwitz class numbers (results from REU)
- “Optimality of an Improved Bound on Pólya’s Positivity Theorem (Univariate Case)”, JMM, January 2020
- “Improved Bound on Pólya’s Positivity Theorem (Univariate Case)”, TAGMaC, November 2018
- (note this research was reframed to relate to Descartes’ Rule of Signs)