Basic Data
Clayton Shonkwiler
Postdoc
Department of Mathematics
University of Georgia
Athens, GA 30602
Email: clayton@math.uga.edu
Office: Boyd 436
Phone: 706.542.2568
Curriculum Vitæ
In the spring of 2012 I am teaching Math 2260. For more information, please see the course web page.
My research is primarily focused on the interplay between topology and geometry. Much of my work is devoted to studying invariants arising from a refinement of the Hodge decomposition theorem for Riemannian manifolds with boundary and to recovering the topology of such manifolds from boundary data. I am also very interested in defining new topological invariants for vector fields which give lower bounds on the field energy; that work has led me to define geometrically meaningful integral formulas for linking invariants and to find homotopy-theoretic interpretations of Milnor’s μ invariants for links. Finally, I am interested in the connections between the geometry of Legendrian knots and the algebraic properties of their Legendrian contact homology; among other things, I have given the first example of a Legendrian knot with nonvanishing contact homology whose Thurston–Bennequin number is not maximal.
If you have any questions, please don’t hesitate to email me.