advising
During summer 2021, Marissa Loving and I organized the 6-week virtual REU Braids, Surfaces, and Low-Dimensional Phenomena. You can see our arXiv preprint here!
Here is our community agreement from the REU.
We advised:
Dane Gollero (University of Utah; graduating Aug 2021)
Viridiana Neri (Columbia University; expected to graduate in May 2023)
Izah Tahir (Georgia Tech; expected to graduate in Dec 2022)
Len White (Cal Poly Pomona; expected to graduate in Dec 2021)
We were supported by NSF grants DMS-1552285 (SK, ML), DMS-1745583 (DG, SK, VN, IT, LW), and DMS-1902729 (ML).
This is a photo/Zoom screenshot from our last day together!
During the summer, we explored 1-bridge braids (an interesting and important class of positive braid knots) and their quantitative properties. This project explicitly determined the braid index of these knots in terms of their defining parameters. Below, you will find a video recording of their (fantastic!) final presentation from the summer, as well as the slides from the presentation (it includes motivation for the project, some beautiful pictures, and an amazing animation!).
Here is their poster presentation from the 2022 (virtual) JMM:
JMM Poster.pdf