My research topic is focused on the Davenport-Heilbronn method over the integers. More specifically I study solvability problems that involve inequalities such as the approximation of a integer by the sum of s monomials with coefficients that are real but not rational. Moreover I am interested in the function field analogue of Waring-like problems. For the past year I have also been working on similar concepts over Z/qZ for a generic integer q.
Talks
Contributing
KMGSC, Lawrence, Kansas, December 7-8, 2024 The Davenport-Heilbronn method for Diophantine Inequalities
32 ÈMES Journées Arithmétiques 2023, Nancy, France, July 3–7, 2023 Solutions to polynomial congruences with variables restricted to a box
Kansas Mathematics Graduate Student Conference, Manhattan, Kansas, April 23, 2022 The Davenport Heilbronn method on Diophantine Inequalities
Departmental
Number Theory Seminar, Manhattan, Kansas, October 23, 2024 Some improvements on the Davenport-Heilbronn method
Student Number Theory Seminar, Manhattan, Kansas, November 10, 2023 An application of Davenport-Heilbronn method, part 2
Student Number Theory Seminar, Manhattan, Kansas, November 3, 2023 An application of Davenport-Heilbronn method, part 1