Advising

UPDATE: We have completed a preprint of the paper that our team wrote building on work that began during the Summer 2021 REU! Take a look here!

During summer 2021, Siddhi Krishna and I organized the 6-week REU Braids, Surfaces, and Low-Dimensional Phenomena.

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 acknowledge support from NSF grants DMS-1552285 (SK, ML), DMS-1745583 (DG, SK, VN, IT, LW), and DMS-1902729 (ML).

Our REU was completely virtual; this is a photo from our last day together.

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.

Here is a video of their final presentation along with their (beautiful!) slideshow. It includes the motivation for the project, a summary of their results, and an amazing animation!

REU2021_FinalPresentation_KnotAMathTalk

Here is their poster presentation from the 2022 (virtual) JMM:

JMM Poster.pdf

Although this summer (2021) is my first time designing and running my own undergraduate REU, I have been engaged in mentoring undergraduate research for some time:

  • Summer 2019 - I was the postdoc mentor for the MSRI-UP undergraduate summer research program in algebraic combinatorics

  • Summer 2018 - I was a graduate student mentor for the Summer@ICERM undergraduate summer research program

    • Project 1: Automorphisms of the k-curve graph

    • Project 2: Length and self-intersection numbers of geodesics in hyperbolic surfaces

  • Spring 2017 - I was a graduate student mentor for the Illinois Geometry Lab

    • Project: Veech Jigsaws