Booth Id:
MATH048
Category:
Mathematics
Year:
2021
Finalist Names:
Zhang, Jessica (School: Proof School)
Abstract:
It is a basic question in contact geometry to classify all non-isotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, this classification is based on the dividing set on the boundary. In my research, I answered the classification question completely for the case of a solid torus by writing down a closed formula for the number of non-isotopic tight contact structures with any given dividing set on the boundary of the solid torus. To do this, I used a novel technique known as bypass induction, in which I showed that bypass attachments could be used to simplify the dividing set. This allowed me to obtain and solve a recurrence relation. Previously, the only fully classified 3-manifold was the 3-ball, and only a few special cases on the solid torus were known by Honda (2000).
Awards Won:
American Mathematical Society: First Award of $2,000
Second Award of $2,000