In mathematics, I am interested in representation theory, quantum groups, algebraic combinatorics, and the connections between these three fields.
Publications:  Lynch, A. G. (2015). The positive even subalgebra of Uq(sl2) and its finitedimensional irreducible modules. Submitted.
 Lynch, A. G. (2015). Cauchy Pairs and Cauchy Matrices. Linear Algebra and its Applications, 471, 320345.
 Bleak, C., Bowman, H., Lynch, A. G., Graham, G., Hughes, J., Matucci, F., & Sapir, J. (2013). Centralizers in R. Thompson's group V_n. Groups, Geometry, and Dynamics, 7(4), 821865.
Conference Presentations:  "FiniteDimensional Irreducible Modules for an Even Subalgebra of Uq(sl2)"
 AMS Fall Central Sectional Meeting, University of WisconsinEau Claire, September 20, 2014
 Symmetries of Graphs and Networks IV, Rogla, Slovenia, July 2, 2014
 Modern Trends in Algebraic Graph Theory, Villanova, PA, June 5, 2014
 "Cauchy Pairs and Cauchy Matrices"
 Rocky Mountain Mathematics Consortium Summer School, University of Wyoming, June 26, 2013
 AMS Spring Sectional Meeting, Iowa State University, April 27, 2013
 Shanghai Conference on Algebraic Combinatorics, Shanghai Jiao Tong University, August 22, 2012
 Graduate Student Combinatorics Conference, University of Illinois at UrbanaChampaign, April 15, 2012
 "Centralizers in R. Thompson's Group V"
 Joint Mathematics Meetings, San Diego, CA, January 2008
 "Arrangements of Affine Hyperplanes in R^k"
 Fall Meeting of the EPADEL Section of the MAA, West Chester University, October 2006

