Research and Notes
My area of research is in geometric structures on manifolds, and specifically rigidity results. In my thesis, I proved that the Euclidean torus cannot be embedded in a holonomy-invariant fashion inside a larger affine manifold. Recently, I have started thinking more about hyperbolic 3-manifolds and in particular, hyperbolic once-punctured torus bundles over circles. Specifically, I've been considering projective rigidity of once-punctured torus bundles at the geometric representation inside the projective representation variety. This has led to think a bunch about twisted cohomology calculations which I have been experimentally verifiying through the use of interval arithemetic and other computational means.
Here are some papers I've work on and notes I wrote that I thought are worth sharing. I'm attempting to get into the habit of .tex-ing up my notes in areas that I find interesting and have the time to do so.
Papers
- Projective Rigidity of Once-Punctured Torus Bundles via the Twisted Alexander Polynomial (2024) [Additional Programs]
- Computer Assisted Projective Rigidity (2024) [Additional Programs]
- Closed Affine Manifolds with an Invariant Line. (in revision)
- Algebraic $k$-systems of Curves. Jonah Gaster, Maxie Lahn, Aisha Mechery, and Simran Nayak. Geometriae Dedicata. 209, 125-134 (2020)