Sean D. Lawton, PhD

Sean D. Lawton, PhD


College of Science

Other Positions:


Research Theme:


Key Interests:

Algebraic Geometry, Associative Rings and Algebras, Differential Geometry, Group Theory and Generalizations, Manifolds and Cell Complexes, Experimental Mathematics


PhD, Mathematics, University of Maryland, College Park

Research Focus

Symmetry is fundamental to our understanding of nature. It is modeled by the mathematical notion of a group. Such groups are difficult to understand and classify. My research program concerns the ways mathematical groups can be understood as geometrically. This geometric study of mathematical groups finds applications in theoretical physics. I approach this subject experimentally, visually, and collaboratively; often including undergraduate and graduate students in projects.

Current Projects

■ Understanding how persistent properties in spaces of geometric avatars of a group tells the nature of the group.

■ Understanding how non-commutative algebraic structures control the geometry of a group’s space of geometric avatars.

■ Experimentally/computationally discovering and verifying conjectures about geometric objects associated to groups.

Select Publications

S. Lawton et al., Homotopy groups of free group character varieties. Ann. Sc. Norm. Super. Pisa Cl. Sci 5(17), 143-185 (2017).

S. Lawton and C. Florentino. The topology of moduli spaces of free group representations. Mathematische Annalen 345, 453-489 (2009).

S. Lawton. Poisson geometry of SL(3,c) – Character varieties relative to a surface with boundary. Trans. Amer. Math. Soc. 361, 2397-2429 (2009).

S. Lawton. Genorators, relations and symmetries in pairs of 3 x 3 unimodular matricies. Journal of Algebra 313(2), 782-801 (2007).



College of Science

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