Circa 2011
Antonio R. Vargas

My CV.
(My email address can be found in there.)

I'm on github. Here's an overview of my repos.
Profile Avatar
2   7   0

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



Statistical Interests

I'm currently working as a researcher in the Oregon Division of Financial Regulation. Outside of my job I'm interested in topics relating to demographics or education. Most of my work is done from a Bayesian perspective.


Mathematical Interests

My mathematical research focused on studying the zeros of polynomials of a single complex variable (locating them, counting them, examining asymptotic distributions in families, etc.). I know a little about the Riemann-Hilbert method of asymptotic analysis and how it relates to these types of problems.


Misc. Notes

21 Jan, 2019 Analyzing suppressed data: Oregon graduation rates by gender, racial and ethnic groups
22 Dec, 2018 Data Analysis: Population Growth in Marion & Polk Counties
12 Dec, 2018 Map: Access to frequent bus routes versus population density in Salem, Oregon
30 Nov, 2018 Data Analysis: Car Crashes in Oregon
6 Oct, 2018 Exploring numerical normal posterior approximation
21 Sep, 2018 Function inference using Gaussian processes
28 Aug, 2018 A note about the asymptotics of entire functions defined by nearly exponential power series [PDF document]
12 May, 2018 Problem Sequence: Calculating a scaling limit for partial sums of the exponential series
7 Feb, 2018

On the distance between zeros of Taylor polynomials of the exponential function, some comments about two problems posed by Zemyan in his 2005 paper on the topic.
15 Sep, 2014

Boundary asympyotics for power series [PDF document], some notes about the growth behavior of power series near their boundary of convergence.
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


Papers

The Saff-Varga Width Conjecture and entire functions with simple exponential growth
Antonio R. Vargas
Constructive Approximation, 49 (2019), No. 2, pp. 307-383.
[SpringerLink, SharedItpreprint (PDF)]

Fixed points of diffeomorphisms on nilmanifolds with a free nilpotent fundamental group
Karel Dekimpe, Sam Tertooy, and Antonio R. Vargas
Preprint.
[arXiv]

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]
(This eventually became the paper titled The Saff-Varga Width Conjecture and entire functions with simple exponential growth, listed above.)


Helpful Userscripts

I wrote a userscript for Math.SE which displays a preview of your comment as you type it.
A detailed description and installation instructions can be found [here].




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 work for a year as a postdoc at KU Leuven. Now I live in Salem, Oregon.



My favorite statistical web pages

Statistical Modeling, Causal Inference, and Social Science
Andrew Gelman and contributors
https://statmodeling.stat.columbia.edu/


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/


My favorite math books

de Bruijn, Asymptotic Methods in Analysis

Marden, Geometry of Polynomials