I got my PhD under the direction of Alex Iosevich from the University of Missouri in 2011. I then held a position as a postdoctoral researcher at the University of Delaware Mathematics Department. I am currently an Assistant Professor at Missouri State University. There are some lecture notes available. You can download a .pdf of my full CV here. Many of my preprints are available on the arXiv. My dissertation is available here. I am a managing editor of the Online Journal of Analytic Combinatorics and I have refereed for the Electronic Journal of Combinatorics.
Spring 2013 - MATH 829
Erdős distance problem, with J. Garibaldi and A. Iosevich, AMS Student Library Series, 56, (2011).
On the number of distinct values of a class of functions with finite domain, with Robert Coulter, (to appear soon in Annals of Combinatorics).
Tracking Time-dependent Scalar Fields with Swarms of Mobile Sensors, with Josh Kirby, Marco Montes de Oca, Louis F. Rossi, and Chien-Chung Shen, Proc. of the 7th IEEE International Conference on Self-Organizing Systems (SASO '13), Philadelphia, PA, USA. T. Holvoet et. al. (Eds.) IEEE Computer Society Press, Los Alamitos, CA, USA, pp. 159--168, (2013).
Distance graphs in vector spaces over finite fields, with D. Hart, A. Iosevich, D. Koh, and Ignacio Uriarte-Tuero, Recent Advances in Harmonic Analysis and Applications, Volume 25, 139-160, (2013).
A note on the multiplicative structure of an additively shifted product set, AA+1, Integers: The Electronic Journal of Combinatorial Number Theory, A34, (2013).
Swarm Interpolation Using an Approxiamte Chebyshev Distribution, with Joshua Kirby, Marco A. Montes de Oca, Louis F. Rossi, and Chien-Chung Shen, 8th International Conference, ANTS 2012, Brussels, Belgium, September 12-14, 2012, Proceedings.
Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems, and distribution of lattice points in convex domains, with Alex Iosevich, (to appear soon in the CANT 2011 proceedings).
On sets of directions determined by fractal subsets of the Euclidean space, with A. Iosevich and M. Mourgoglou, Journal d'Analyse Mathematique 116 (1), 355-369, (2012).
An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries, with D. Covert, D. Hart, A. Iosevich, and I. Uriarte-Tuero, Discrete Math. 311, no. 6, 423-430, (2011).
A low complexity replacement scheme for erased frame coefficients, with Bernhard Bodmann, Peter G. Casazza, and Gitta Kutyniok, Proceedings of SPIE, Wavelets XIII, San Diego (2009) pp. 744600-1-10.
Error correction for erasures of quantized frame coefficients, with Bernhard Bodmann, Peter G. Casazza, and Gitta Kutyniok, Proceedings of SAMPTA (2009), http://www.latp.univ-mrs.fr/SAMPTA09.
Orthogonal systems in vector spaces over finite fields, with A. Iosevich, Electronic J. of Combinatorics, Volume 15, December (2008).
Acquiring and maintaining abstract landmark chunks for cognitive robot navigation, with R. H. Luke, J. M. Keller, and M. Skubic, Intelligent Robots and Systems, 2005. (IROS 2005). 2005 IEEE/RSJ International Conference on.
May 22, 2013, CUNY - Combinatorial and Additive Number Theory Conference A multi-scale approach to the Erdős-Falconer type single distance problems lecture notes
May 23, 2012, CUNY - Combinatorial and Additive Number Theory Conference Combinatorial estimates of the size of an image set
October 20, 2011, Gettysburg College - Math Colloquium Brothers and laser beams: a brief peek at incidence geometry via graph theory
May 27, 2011, CUNY - Combinatorial and Additive Number Theory Conference Consequences and connections of recent results in geometric combinatorics
March 24, 2011, Indiana University On the relationships between several problems in geometric combinatorics
December 10, 2010, Rochester Institute of Technology - IEEE Meeting From design to implimentation: Vision and VLSI
December 6, 2010, University of British Columbia - CMS Meeting Some connections between discrete and continuous geometric combinatorics, with recent illustrative results-- sharpness examples.
November 10, 2010, University of Rochester Geometric interactions with some problems in additive number theory.
October 15, 2010, CUNY - Graduate Seminar Elementary proof of Elekes's sums and products result. lecture notes
October 14, 2010, CUNY Some connections between discrete and continuous geometric combinatorics, with recent illustrative results-- hinge estimates.
May 27, 2010, CUNY - Combinatorial and Additive Number Theory Conference Sharpness of Falconer's estimate, geometric incidence theorems, and distribution of lattice points in convex domains, II.
May 21, 2008, CUNY - Combinatorial and Additive Number Theory Conference Orthogonal systems in vector spaces over finite fields.
February 2012, University of Maryland, Norbert Wiener Center - February Fourier Talks Reliability of swarming alrogithms for mobile sensor network applications lecture notes
February 2009, University of Maryland, Norbert Wiener Center - February Fourier Talks Orthogonal systems in vector spaces over finite fields