Summer Term 2020

  1. Deeply slice knots (joint with Michael Klug): Knots in the boundary of a 4-manifold W which bound a properly embedded disk in W, but which are not null-concordant in a collar neighborhood \partial W x [0,1] of the boundary.
    Deeply Slice Knots (.pdf, handwritten notes)
  2. Finger-Whitney Unknotting Numbers (joint with Jason Joseph, Michael Klug, Hannah Schwartz): Inspired by Schneiderman-Teichner's perspective on Gabai's 4-dimensional light bulb theorem we define the Finger-Whitney unknotting number of knotted 2-spheres in S^4: Since every 2-knot K in S^4 can be obtained by first performing a number of (trivial) finger moves on the unknot, and in a next step removing the resulting intersection points in pairs via Whitney moves (along possibly complicated discs), we can define u_Wh(K) as the minimal number of finger moves needed in such a process to arrive at K. We are trying to relate this to the 1-handle stabilization number and looked specifically at examples of ribbon 2-knots and twist-spins of classical knotted arcs.
    Finger-Whiteney Unknotting Numbers (.pdf, handwritten slides), Finger-Whiteney Unknotting Numbers - Part 2 [Michael] (.pdf, handwritten slides)
  • Topological Spring School, Matemale, October, 2020 (?)

Winter Term 2019/2020

  • Winter Braids X, Pisa, February 17 - 21, 2020
  • Low-dimensional topology workshop, Regensburg, October 21 - 23, 2019.

Summer Term 2019


Winter Term 2018/2019

Summer Term 2018

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2018.

Winter Term 2017/2018

Summer Term 2017

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2017.
  • Handout (.pdf) for a talk on the First Lie Theorem.

Summer Term 2016


Links: Github, MathStackExchange, Blog.