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Most of my research thus far has been focused on 3D contact topology. In particular I have been working explicitly with characteristic foliations of convex surfaces embedded in 3-dimensional contact manifolds. If I am allowed to be a bit more broad in what I find interesting, I would say I enjoy contact and symplectic topology in general, as well as low-dimensional topology and (at least some ideas of) knot theory.
Things I wrote:
- (Co)tangent Things (updated: 2018-05-08)
We explore the tangent and cotangent bundle associated to manifolds. It culminates with de Rham cohomology and some integration on manifolds.
- A little about Gram-Schmidt (updated: 2019-09-09)
A little about the Gram-Schmidt alogrithm and a version for symplectic bilinear forms.
- Camels and symplectic rigidity in vector spaces (updated: 2019-09-11)
It's about camels...and I guess symplectic vector spaces. We prove the affine version of the non-squeezing theorem.
- Characteristic classes (updated: 2019-12-31)
Characteristic classes. Roughly based on the contents of Tu's book introducing the topic. I tried my best to make it accessible to those who have read my cotangent things pdf. It's not quite finished yet.
- Gel'fand and his algebras (updated: 2020-08-07)
I compiled this overview of the history and theory of Gel'fand's theory for my functional analysis class the past spring. Maybe you might want to read it.
- The Gromov-Lawson obstruction and the Geroch conjecture (updated: 2021-09-28)
I compiled this two-source overview on the application of index theory and spin geometry to prove the so-called Geroch conjecture: that $T^n$ does not admit a metric with positive scalar curvature. Details are sparse.