Circa 2011
Antonio R. Vargas

Ph.D. Candidate

Chase Building, Room 226
Department of Mathematics and Statistics
Dalhousie University
Halifax, Nova Scotia, B3H 4J5

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

My CV.

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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.). Right now I'm learning a little about the Riemann-Hilbert method of asymptotic analysis and how it relates to these types of problems.

Upcoming Events

July 2016 - Thesis defense

July 2017 - 14th International Symposium on Orthogonal Polynomials, Special Functions, and Applications at the University of Kent, UK


Newman-Rivlin asymptotics for partial sums of power series
A. R. Vargas

Limit curves for zeros of sections of exponential integrals
A. R. Vargas
Constructive Approximation, 40 (2014), No. 2, pp. 219-239.
[SpringerLink, arXiv]

Zeros and convergent subsequences of Stern polynomials
A. R. Vargas
Journal of Mathematical Analysis and Applications, 398 (2013), No. 2, pp. 630–637.
[ScienceDirect, arXiv]

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

MSc. Thesis

Zeros of Sections of Some Power Series

Misc. Notes

23 Feb, 2014 On calculating a "Mathematically Correct Breakfast", a post about the surface area exposed after cutting a bagel into two interlocking rings
18 Feb, 2013 An animation of the zeros of sections of exponential integrals, an interesting plot that relates to my master's thesis
25 July, 2011 Asymptotic bound for a particular sum, answering a question of Qiaochu Yuan


Originally from Laguna Niguel, California, I received my BA in mathematics from California State University, Fullerton after changing majors from computer science. At Fullerton I studied under the guidance of Alain Bourget and Tyler McMillen. I then lived in Toronto, Ontario for a short while before heading to Halifax, Nova Scotia to study at Dalhousie University. My supervisor here is Karl Dilcher.

My favorite mathematical web page

The Beauty of Roots
John Baez

Some papers I have enjoyed reading

A sum over the zeros of partial sums of exp(x)
C. Yalçin Yildirim
Ramanujan Mathematical Society, 6 (1991), No. 1-2, pp. 51-66.

On the number of distinct zeros of polynomials
M. S. Klamkin and D. J. Newman
The American Mathematical Monthly, 66 (1959), No. 6, pp. 494-496.

Finite Calculus: A Tutorial for Solving Nasty Sums
David Gleich

My favorite math books

de Bruijn, Asymptotic Methods in Analysis

Marden, Geometry of Polynomials

Halmos, Naive Set Theory