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.

I'm also on Math.StackExchange:

Math.StackExchange is a questions and answers site for mathematics.

You can visit the front page to see some of the recently active questions.

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

Papers

Newman-Rivlin asymptotics for partial sums of power series

A. R. Vargas

(preprint)

[arXiv]

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

[arXiv]

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 |

Background

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

http://math.ucr.edu/home/baez/roots/

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.

[pdf]

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.

[JSTOR]

Finite Calculus: A Tutorial for Solving Nasty Sums

David Gleich

[pdf]

My favorite math books

de Bruijn, Asymptotic Methods in Analysis

Marden, Geometry of Polynomials

Halmos, Naive Set Theory