profile for Antonio Vargas at Mathematics, Q&A for people studying math at any level and professionals in related fields
Antonio R. Vargas

Masters student

Chase Building, Room 226
Department of Mathematics and Statistics
Dalhousie University
Halifax, Nova Scotia B3H 1Z9

antoniov (at) mathstat (dot) dal (dot) ca

My CV.



Research Interests

I'm primarily interested in studying the zeros of polynomials of a single complex variable (locating them, counting them, examining asymptotic distributions in families, etc.) from the standpoint of classical analysis.


Papers

Zeros and convergent subsequences of Stern polynomials
A. Vargas
(submitted)
[arXiv]

Interlacing and non-orthogonality of spectral polynomials for the Lamé
operator
A. Bourget, T. McMillen, and A. Vargas
Proceedings of the American Mathematical Society, 137 (2009), No. 5, pp. 1699–1710.
[AMS, arXiv]



Misc. Notes

Asymptotic bound for a particular sum, answering a question of Qiaochu Yuan



Background

I received my BA in mathematics from California State University, Fullerton.



Some cool web pages

The Beauty of Roots
John Baez
http://math.ucr.edu/home/baez/roots/


Some cool papers by other people

On the number of distinct zeros of polynomials
M. S. Klamkin and D. J. Newman
The American Mathematical Monthly66 (1959), No. 6,  pp. 494-496.
[JSTOR]

Finite Calculus: A Tutorial for Solving Nasty Sums
David Gleich
[pdf]


Some cool books

Marden, Geometry of Polynomials

Halmos, Naive Set Theory

Alexandroff, Elementary Concepts in Topology

Olds, Continued Fractions

Kazarinoff, Geometric Inequalities