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The search for highly distinguishing quandles for classical knots
Geometry/Topology| Speaker: | Peyton Wood, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, May 20 2025, 2:10PM |
One topic of great interest the last 25 years is finding a small set of quandles which can distinguish all knots of crossing number n and lower (up to reversal and mirror imaging). One could conjecture that for all n it may take only one, possibly quite large and complex, quandle to do this task. In this talk we explore finding such quandles for small crossing numbers, discuss the underlying behavior of this class of quandle, and briefly explain how one may try and find such quandles for larger crossing numbers, or failing to do so, find relatively small sets of quandles which accomplish this task. Recently, authors have used so-called Quandle Rings to do this, but studying the transvection group of a quandle may be the key insight to push this field forward. Work joint with Quinn McMichael Salix.