My PhD and ongoing research is in real algebraic geometry / symbolic computation with 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.
Background:
- 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.
Publications:
- Dissertation
- Elliptic curves, modular forms, and sums of Hurwitz class numbers (results from REU)
Talks:
- “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)