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for experts:
I study low-dimensional topology and geometric topology. In particular, I study 3- and 4- dimensional manifolds by studying the geometric structures they admit (like taut foliations), as well as the knots and surfaces they contain. I'm usually trying to build manifolds admitting a specific type of geometric structure or topological property. I often use braids as a lens to explore 3- and 4-manifolds.
for everyone:
Topology is the study of shapes and spaces. Mathematicians (like other scientists) try to study hard problems by breaking them up into smaller, more digestable pieces. Some spaces (like a ream of paper) can be decomposed into "slices" -- in this case, the slices are the sheets of paper themselves. Surprisingly, not all objects can sliced up! Determining when this behavior does and doesn't happen is one of my many research goals. I also like studying knotted up objects, like braids and surfaces.
publications & preprints
publications & preprints
All of my pure mathematics research publications are publicly available on the arXiv, and here is my Google Scholar page.
In pure mathematics, co-authors are listed alphabetically by last name. Undergraduate coauthors are denoted by (*).
Twist positivity, L-space knots, and concordance
Twist positivity, L-space knots, and concordance
21 pages, joint with Hugh Morton.
Selecta Mathematica. 31 (1) (2025) Paper No. 11. [arxiv, pdf, journal, lecture recording from ICERM in July 2024]
n-bridge braids and the braid index
n-bridge braids and the braid index
15 pages, joint with Dane Gollero*, Marissa Loving, Viridiana Neri*, Izah Tahir*, Len White*
Journal of Knot Theory and its Ramifications. 32 (13) (2023), 2350090 (22 pp.) [arxiv, pdf, poster]
Reflections on running an REU (with an eye towards equity).
Reflections on running an REU (with an eye towards equity).
joint with Marissa Loving.
Notices of the AMS, Vol. 69 (2) (2022), 216-220 [pdf]
Brunnian exotic surface links in the 4-ball
Brunnian exotic surface links in the 4-ball
40 pages, joint with Kyle Hayden, Alexandra Kjuchukova, Maggie Miller, Mark Powell, and Nathan Sunukjian
Giving to whom? Altruism in different types of relationships.
Giving to whom? Altruism in different types of relationships.
joint with Peter DeScioli.
Journal of Economic Psychology 34 218-228 [pdf]
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