**Tim Bates**
Hi I'm Tim and I'm a third year PhD. student at Rutgers New Brunswick. I like thinking about manifolds of dimensions up to and including 4.
More concretely I am interested in knots, knotted surfaces, Heegaard-Floer homology and its consequences. In particular, I have been thinking a lot about freely periodic knots.
I attended Texas A&M University from 2019 to 2023
where I completed a B.S. and M.S. degree in Mathematics with a minor in physics. I was also an organizer for the 2026 Graduate Student Topology and Geometry Conference!
Preprints
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I wrote an article together with Aakash Parikh on the
knot Floer homology of Freely 2-periodic knots and their quotients: LINK HERE
CV
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Here you can find a link to my CV: LINK
Masters thesis
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I wrote a masters thesis where I explored some of the literature about Thurston polytopes!
![Figure [TP1]: L14a29515 and its Thurston Polytope.](https://timgbates.github.io/document/Thurstonpoly.png width="300px" border="1")
Notes and Other Writings
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I try to type up a lot of the things that I learn. Here you can find links to some of the things I've typed.
## Misc. Algebra and Analysis
Links
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Some Older Projects:
- Thurston Polytopes
- Uniform Acceleration
Here are links to some cool resources.
Topology Related Links
Other
Research and Projects
Misc. Expository Notes
Fun Facts
Best Invariants
- Euler Characteristic (especially of the brain): I wrote a short python code for computing the Euler Characteristic of a graph: HERE
It computes the graphs's associated clique complex's Euler characteristic via Oliver Knill's discrete Gauss-Bonnet theorem.
- Thurston Norm Ball (for obvious reasons)
Favorite Papers
- Topological Phase transitions in functional Brain Networks by Santos et. al.
- Classical Roots of the Unruh and Hawking Effects by Pauri and Vallisneri
Useful Links (pun intended)
Other Links