Antonio
R. Vargas

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.

Papers

Fixed points of diffeomorphisms on nilmanifolds with a free nilpotent fundamental group

Karel Dekimpe, Sam Tertooy, and Antonio R. Vargas

In preparation.

The Saff-Varga Width Conjecture and entire functions with simple exponential growth

Antonio R. Vargas

Submitted, in review.

Limit curves for zeros of sections of exponential integrals

Antonio R. Vargas

Constructive Approximation, 40 (2014), No. 2, pp. 219-239.

[SpringerLink, arXiv]

Zeros and convergent subsequences of Stern polynomials

Antonio 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

Alain Bourget, Tyler McMillen, and Antonio R. Vargas

Proceedings of the American Mathematical Society, 137 (2009), No. 5, pp. 1699–1710.

[AMS, arXiv]

PhD. Thesis

Scaling Limits for Partial Sums of Power Series

[arXiv]

MSc. Thesis

Zeros of Sections of Some Power Series

[arXiv]

Rejected Papers

Newman-Rivlin asymptotics for partial sums of power series

A. R. Vargas

[arXiv]

Helpful Userscripts

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A detailed description and installation instructions can be found [here].

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 under the supervision of Karl Dilcher. After completing my PhD I moved to Belgium to take a position as a postdoc at KU Leuven.

My favorite mathematical web pages

Roots, Schottky semigroups, and Bandt’s Conjecture

Danny Calegari

https://lamington.wordpress.com/2014/12/21/roots-schottky-semigroups-and-bandts-conjecture/

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