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Independent Study supervision:
Independent Study supervision:
Frontiers in geometric topology
In Summer 2024, I supervised Zheheng (Tony) Xiao (Columbia '25) through the Columbia Rabi Scholars program. We studied geometric topology in dimensions 3 and 4, with a focus on braids in 4-dimensions. We also developed some of the skills required to read research papers in pure math. In Fall 2025, Tony will begin his PhD studies at Princeton's Program in Applied and Computational Mathematics.
A hands-on approach to low-dimensional topology
In Spring 2023, I supervised Alison Tatsuoka (Columbia '23) and Aaron Cohen (Columbia '24) in an independent study on fundamental topics in low-dimensional topology. We focused on constructing examples and hands-on computations. Alison is currently a PhD student at Princeton, working with Dave Gabai, and she recently received the NSF GRFP!
Summer 2021 REU supervision:
Summer 2021 REU supervision:
This is a photo/Zoom screenshot from our last day together!
During summer 2021, Marissa Loving and I organized the 6-week virtual REU Braids, Surfaces, and Low-Dimensional Phenomena. The paper produced from this REU has been published at The Journal of Knot Theory and its Ramifications! We were supported by NSF grants DMS-1552285 (SK, ML), DMS-1745583 (DG, SK, VN, IT, LW), and DMS-1902729 (ML).
We advised:
Dane Gollero (University of Utah '21; current: PhD student at Wisconsin-Madison with an NSF GRFP.)
Viridiana Neri (Columbia University '23)
Izah Tahir (Georgia Tech '22)
Len White (Cal Poly Pomona '21; current: PhD student at Portland State)
Here is our community agreement from the REU.
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. A video recording of their (fantastic!) final presentation from the summer is below, as are the slides from the presentation (which includes motivation for the project, some beautiful pictures, and an amazing animation!).
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