Most of my research attention is devoted to number theory from an analytic perspective (which is different from analytic number theory), where my interests include Diophantine approximation, Thue equations, polynomial root separation, and other topics.
I have given several versions of the same talk on my research into
Thue equations.
All have been titled something like "Bounds on the Number of
Solutions to Thue's Inequality."
The slides for the best version of the talk (which was given
in the PIMS Emergent Research Seminar on October 11, 2023) are
here: thue_equation_talk.pdf. Moreover, the talk was recorded, and you can view the talk here: https://mathtube.org/lecture/video/bounds-number-solutions-thue-equations.
While I have given talks about my work on polynomial root separation, none of them contain the substantial progress I made with Chi Hoi Yip in the paper above. As such, I won't link to any slides or recordings here.
I spoke about my research on products of powers of algebraic integer conjugates (joint work with Seda Albayrak, Samprit Ghosh, and Khoa Nguyen) at the most recent Alberta Number Theory Days conference at the Banff International Research Station on March 23, 2024. You can find the slides here: exp_inequalities_talk.pdf. Moreover, the talk was recorded, and you can view the talk here: https://www.birs.ca/events/2024/2-day-workshops/24w2020/videos/watch/202403231735-Knapp.htmlI did my master's thesis under Colin McLarty
at Case Western Reserve University in
2017.