Surfaces bounded by knots in the 3-sphere

Research Horizons Seminar
Wednesday, November 10, 2021 - 12:30pm for 1 hour (actually 50 minutes)
Skiles 006
Jonathan Simone – Georgia Institute of Technology – jsimone7@gatech.edu
Christopher DuPre

Given a knot $K$ in the 3-sphere, one can ask: what kinds of surfaces in the 3-sphere are bounded by $K$? One can also ask: what kinds of surfaces in the 4-ball (which is bounded by the 3-sphere) are bounded by $K$? In this talk we will discuss how to construct surfaces in both the 3-sphere and in the 4-ball bounded by a given knot $K$, how to obstruct the existence of such surfaces, and explore what is known and unknown about surfaces bounded by so-called torus knots.