Research

My research interests are mainly focused on knotted surfaces in S^4, in particular ribbonness, concordance, bridge trisections, and various algebraic aspects of knot theory such as Alexander ideals and quandles.

Awards:

  • B.J. Ball Scholarship (link)
    • 2018
    • 2017
    • 2016
    • 2015

Invited Talks:

  • 0-concordance of knotted surfaces and Alexander ideals; Unifying 4-dimensional Knot Theory, BIRS, Banff Canada, November 2019
  • The Ribbon Genus of a Knotted Surface; GA Tech Topology Seminar, October 2018
  • Quandle Invariants via Bridge Trisections; AMS Special Session, Northeastern University, April 2018
  • The Fundamental Quandle of a Bridge Trisected Surface; Winter Trisectors Meeting, University of Georgia, February 2018

Contributed Talks:

  • Quandle Invariants via Bridge Trisections; Knots in Washington XLVII, George Washington University, January 2019
  • Ribbon Genus, Virtual Graphs, and Wirtinger Deficiency; Topology Students Workshop, Georgia Tech June 2018
  • Ribbon Genus, Virtual Graphs, and Wirtinger Deficiency; GSCAGT, Temple University, June 2018

Talks:

  • Knotted Surfaces and Connected Sums; UGA Grad Student Seminar, August 2018
  • The Commutative Monoid of Exotic R^4’s; UGA Grad Student Seminar, Jan 2018
  • Infinite Order Corks; UGA Grad Student Seminar, Nov 2017
  • Quandle Colorings and Knotted Surfaces; UGA Mock AMS Conference, July 2017
  • The Alexander Invariant; UGA Mock AMS Conference, July 2016
  • The Map Color Theorem; UGA Graduate Student Seminar, Fall 2015
  • Zero Free Intervals of Chromatic Roots; UGA Mock AMS Conference, July 2015

Conferences attended:

  • Knots in Washington XLVII; George Washington University, Jan. 2019
  • Knotted Surfaces in 4-manifolds; UMass Amherst, October 2018
  • Topology in Dimensions 3, 3.5, and 4, UC Berkeley, June 2018
  • Topology Students Workshop, Georgia Tech, June 2018
  • Graduate Student Conference in Algebra, Geometry, and Topology, Temple University, June 2018
  • AMS Special Session: Connections between Trisections of 4-Manifolds and Low Dimensional Topology, Northeastern University, April 2018
  • Winter Trisectors Meeting, University of Georgia, February 2018
  • Tech Topology Conference, Georgia Tech, December 2017
  • 2017 Georgia International Topology Conference, UGA, May 2017
  • Trisections and Low-Dimensional Topology, AIM, March 2017
  • Tech Topology Conference, Georgia Tech, December 2016
  • Georgia Topology Conference, UGA, May 2016
  • AMS Spring Southeastern Sectional Meeting, UGA, March 2016
  • Tech Topology Conference, Georgia Tech, December 2015
  • Georgia Topology Conference, UGA, June 2015
  • Tech Topology Conference, Georgia Tech, December 2014
  • UGA Topology Seminar, Fall 2014 – Present
  • UGA Geometry Seminar, Spring 2015 – Present