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Kellen Myers - Homepage

Office: Hesler 424,
Office Hours: None,
Email: kellen.myers [at] gmail [dot] com

Welcome to my homepage.

I am a Research Associate in the Fefferman Lab at the University of Tennessee (Knoxville), affiliated with the Departments of Mathematics and Ecology & Evolutionary Biology and with the National Institute of Mathematical and Biological Synthesis (NIMBioS). I completed my PhD in Mathematics at Rutgers University where my advisor was Doron Zeilberger . I hope you enjoy my website.

Kellen Myers & Aaron Robertson, Two Color Off-Diagonal Rado-Type Numbers, Electronic Journal of Combinatorics, 14(1), R53.
[abstract] [PDF file] [arXiv preprint] [El. J. Comb. journal] [Aaron Robertson person]

My mathematical research mainly falls into two areas: computational discrete mathematics and mathematical biology.

My combinatorial research interests 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. I am also interested in analytical methods in Diophantine Ramsey theory, which really means number theory and additive combinatorics, but from a non-typical point-of-view.

My research in mathematical biology focuses on the transient dynamics of ecological and epidemiological systems. The goal is to understand, characterize, explain, and even predict phenomena that arise in unstable and complex biological systems that can be modelled by some mathematical object. One particular area of interest is the dynamics of invasive, endangered, or evolutionarily adaptive populations coupled with the dynamics of an epidemiological system.

My passion for these areas of research may result in very different work, but it is a single passion, rooted in the challenges in constructing, implementing, and analyzing complex computational programs or models, as well as the excitement when these methods yield results.

I also enjoy problems and methods from other areas, like set systems or game theory. I would characterize my interest in mathematics, in general, as very broad. I enjoy the interdisciplinary nature of mathematics and appreciate collaboration between mathematicians with diverse interests, and between mathematicians and people in other areas of scholarship. I am also a proponent of computer-based pedagogy and active learning in the mathematics classroom and have been recognized for my excellence and innovation as an educator.

Lastly, my Erdős number is 3 (check here ).

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Kellen Myers & Aaron Robertson, Two Color Off-Diagonal Rado-Type Numbers, Abstract:

We show that for any two linear homogeneous equations E0, E1, 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(E0; E1) to be the smallest N such that [1,N] must admit such solutions. We determine a lower bound for RR(E0, E1) in certain cases when each Ei is of the form a1x1 + ... + anxn = z as well as find the exact value of RR(E0, E1) when each is of the form x1 + a2x2 + ... + anxn = 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.

Kellen Myers & Aaron Robertson, Two Color Off-Diagonal Rado-Type Numbers, Abstract:

There exists a minimum integer N such that any 2-coloring of {1, 2, ... , N} admits a monochromatic solution to x+y+kz = lw 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.

K. Myers → A. Robertson → T. C. Brown → P. Erdős