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Welcome to my homepage. I am a Mathematics PhD student at Rutgers University. My advisor is Doron Zeilberger. By the usual mathematicians' convention, this site is perpetually under construction. For now, feel free to read any of the papers below.

We show that for any two linear homogeneous equations E_{0}, E_{1}, each with at least
three variables and coefficients not all the same sign, any 2-coloring of Z^{+} admits
monochromatic solutions of color 0 to E0 or monochromatic solutions of color 1 to E1.
We define the 2-color off-diagonal Rado number RR(E_{0}; E_{1}) to be the smallest N such
that [1,N] must admit such solutions. We determine a lower bound for RR(E_{0}, E_{1})
in certain cases when each E_{i} is of the form a_{1}x_{1} + ... + a_{n}x_{n} = z
as well as find the exact value of RR(E_{0}, E_{1}) when each is of the form
x_{1} + a_{2}x_{2} + ... + a_{n}x_{n} = z. We then present a Maple package
that determines upper bounds for off-diagonal Rado numbers of a few particular types, and use it to quickly prove
two previous results for diagonal Rado numbers.

There exists a minimum integer N such that any 2-coloring of {1, 2, ... , N} admits a
monochromatic solution to x+y+kz = *l*w for k,*l* in Z^{+}, where N depends on k and *l*.
We determine N when *l*-k is in {0, 1, 2, 3, 4, 5}, and for all k, *l* for which
(1/2)((*l*-k)^{2} -2)(*l*-k+1) ≤ k ≤ *l* - 4, as well as for arbitrary k when *l* = 2.

- Kellen Myers &
Aaron Robertson,
Two Color Off-Diagonal Rado-Type Numbers,
^{[abst]}*Electronic Journal of Combinatorics***14(1)**, R53. - Kellen Myers & Aaron Robertson,
Some Two Color, Four Variable Rado Numbers,
^{[abst]}*Advances in Applied Mathematics***41 (2)**, 214-226.

My research interests are in combinatorics. The problems I work on are in the area of Ramsey theory, in particular Diophantine Ramsey theory, the study of the Ramsey-theoretic properties of the integer solutions to equations. My research focuses on computer-diven methods, but I am also interested in analytical methods in Diophantine Ramsey theory, which is to say additive combinatorics. I also enjoy problems and methods from other areas, like hypergraph theory and game theory. I would characterize my interest in mathematics, in general, as very broad. There are many topics of mathematics that I find very compelling, although I only have a basic familiarity with them. I enjoy the interdisciplinary nature of mathematics and appreciate collaboration between mathematicians with diverse interests. I am also a proponent of computer-based pedagogy and active learning in the mathematics classroom. Also, my Erdős number is 3 (check here).

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