Faculty & Staff Directory
- Founder, Mason Experimental Geometry Lab
PhD, Mathematics, University of Maryland, 2006
Sean Lawton serves as a Professor in the Department of Mathematical Sciences at George Mason University where he is the founder of the Mason Experimental Geometry Lab — an experimental research lab in mathematics.
Sean and his team of undergraduate and graduate students not only conduct experimental research and visualization projects, but are also involved in hands-on outreach activities about mathematics to K-12 schools in the George Mason University area.
Symmetry appears throughout nature, and natural phenomena are often explained via symmetry. Symmetry is encoded mathematically with the notion of a "group". Groups are difficult to classify and distinguish from each other. Each group admits many avatars called "representations". This collection of representations of a group is called a "character variety". Character varieties themselves have a shape and so have symmetries. One of my current research projects concerns organizing and classifying groups by the shape (topology) of their character varieties. Another current research project concerns understanding the symmetries of character varieties through dynamical systems
Vertically integrated research, education and workforce training through geometry labs. Community building, outreach, and engagement.
Courses Taught: Geometry, Topology, and Algebra courses at the undergraduate and graduate level.
- The mapping class group action on SU(3) -character varieties (with William Goldman, Eugene Xia), Ergodic Theory and Dynamical Systems (2020), 1-15
- Homotopy groups of character varieties of free groups (with Carlos Florentino, Daniel Ramras), Ann.Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017), no. 1, 143185
- The topology of moduli spaces of free group representations (with Carlos Florentino), Mathematische Annalen, 345 (2009), No. 2, 453-489
- Poisson Geometry of SL(3, C)-Character Varieties Relative to a Surface with Boundary, Transactions of the American Mathematical Society, 361 (2009), No. 5, 2397-2429
- Generators, relations and symmetries in pairs of 3 × 3 unimodular matrices , Journal of Algebra Volume 313 (2007), Issue 2, Pages 782-801
- 2020 Teaching Excellence Award
- 2020 Mentoring Excellence Award
- Simons Collaboration Grant, 2018-2023
- Simon’s Collaboration Grant, 2012-2017
- NSF-DMS Research Grant, 2013-2016