SMRI Seminar ’The generalized knot complement problem’ Dave Futer (Temple University, Philadelphia) Date and time: Thursday 2 May, 13:00-14:00 AEST Location: Law Annex Lecture Theatre 026 and online Register/join for online attendance: https://uni-sydney.zoom.us/j/82819441564 Abstract: In 1908, Tietze posed the provocative question of whether a mathematical knot - a knotted rope, with its ends spliced together - is completely determined by the topological shape of the empty space that surrounds the knot. After being open for 80 years, this question was solved in 1988, and we know the answer is Yes. Since that time, mathematicians have studied the open question of whether the same property holds for knots in general 3-dimensional spaces. Given a 3-dimensional manifold M, is a knot in M entirely determined by the space that surrounds it in M? I will discuss some recent work on this question using hyperbolic (negatively curved) geometry. This is joint work with Jessica Purcell and Saul Schleimer. ---- Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on the SMRI Terrace (accessed through A14-04-L4.36) ---- Current and past seminar info (including recordings) can be found on the seminars webpage. Other upcoming SMRI events can be found here: https://mathematical-research-institute.sydney.edu.au/news-events/ SMRI YouTube Channel: https://youtube.com/@SydMathInst