Antonio has moved!

I am now a postdoc at KU Leuven in the Section of Analysis. Until I get my webpage set up over there I'll keep this one more or less up to date. Eventually this will forward to my new page at KUL.





Circa 2011
Antonio R. Vargas

Postdoctoral Fellow at Katholiek Universiteit Leuven

Departement Wiskunde
Celestijnenlaan 200B bus 05.31
3001 Leuven
Belgium

antonio (dot) vargas (at) kuleuven (dot) be

My CV.

I'm also on Math.StackExchange:
profile for Antonio Vargas at Mathematics, Q&A for people studying math at any level and professionals in related fields
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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

November 2016 - Workshop on Orthogonal Polynomials and Special Functions in Copenhagen, Denmark

December 2016 - XII Brunel – Bielefeld Workshop on RMT at Brunel University, UK

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


Papers

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]


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]


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 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