SheaI’m an Associate Professor of Mathematics at Louisiana State University. Before arriving at LSU, I was a NSF Postdoctoral Fellow at Columbia University and a Ph.D. student at the University of Pennsylvania. I received my doctorate back in 2009 under the supervision of John Etnyre and Herman Gluck.

My research centers on questions in contact geometry, low-dimensional topology, knot theory and Riemannian geometry. My work addresses classification and structure problems for contact 3-manifolds as well as the Legendrian and transverse knots they contain. I am also interested in questions lying in the intersection between classical knot theory and Riemannian geometry. I study geometric invariants in magnetohydrodynamics and, specifically, higher-order analogues of helicity invariants of vector fields.

Teaching: This summer, I am teaching a course on Elementary Differential Equations. I most recently recently taught a graduate course on Riemannian geometry. In 2012 I received the Chauvenet Prize for expository mathematical writing at the Joint Meetings. I was awarded the prize together with my coauthors Dennis DeTurck, Herman Gluck and Daniel Pomerleano for our article The Four Vertex Theorem and its Converse.

〈Sci|State〉: 〈Sci|State〉 is Scott Baldridge’s and my attempt to create a space where world-class scientists can discuss their latest research. We’ll be keeping the discussion at the general interest level. We’ll be posting content accessible to students, teachers and researchers alike.  Please take a look and, if you like what you see, Like our Facebook page and Subscribe to our YouTube channel.

My Postdoctoral Mentees:
C.-M. Mike Wong

My Current Graduate Students:
– Federico Salmoiraghi
Ryan Leigon (co-advisor with Scott Baldridge)
Rima Chatterjee
– Sudipta Ghosh (co-advisor with Scott Baldridge)
– Robert Quarles (co-advisor with Oliver Dasbach)

My Past Graduate Students
– Jose Ceniceros, Ph.D. Louisiana State University, 2017.
• Thesis: Legendrian and Transverse Invariants Coming from Knot Floer Homology
• Currently an Assistant Professor at Hamilton College