Faculty & Staff Directory
Sean Lawton
- Professor
- Founder, Mason Experimental Geometry Lab
Contact Info
- Name
- Dr. Sean D. Lawton
- Job Title
- ProfessorFounder, Mason Experimental Geometry Lab
- Website
- Phone Number
- Office Number
- Exploratory Hall, Room 4413, MSN 3F2
Affiliations
Departments
- Mathematical Sciences Department ()
- Mathematical Sciences Department (Instructional Faculty)
Other Affiliations
- Institute for Digital Innovation https://idia.gmu.edu
- Math Alliance https://www.mathalliance.org
- Geometry Labs United http://geometrylabs.net
- GEAR http://gear.math.illinois.edu
Centers
- Mason Experimental Geometry Lab (MEGL)
Research Areas
- Algebraic Geometry
- Associative Rings and Algebras
- Group Theory and Generalizations
- Manifolds and Cell Complexes
Education
PhD, Mathematics, University of Maryland, 2006
About
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.
Current Research
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
Teaching Focus
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.
Selected Publications
- Bad Representations and Homotopy of Character Varieties (with Clément
Guérin, Daniel Ramras), Annales Henri Lebesgue, Volume 5 (2022), pp. 93-140 - 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
Awards
- 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
Videos of Sean Lawton
Contact Info
- Name
- Dr. Sean D. Lawton
- Job Title
- ProfessorFounder, Mason Experimental Geometry Lab
- Website
- Phone Number
- Office Number
- Exploratory Hall, Room 4413, MSN 3F2