# 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