Mathematics Research

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 finite-dimensional irreducible modules. Submitted.
• Lynch, A. G. (2015). Cauchy Pairs and Cauchy Matrices. Linear Algebra and its Applications, 471, 320-345.
• 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), 821-865.

Conference Presentations:

• "Finite-Dimensional Irreducible Modules for an Even Subalgebra of Uq(sl2)"
  • AMS Fall Central Sectional Meeting, University of Wisconsin-Eau 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 Urbana-Champaign, 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