Research

I am thinking about Seiberg-Witten Theory and Near-Symplectic Geometry. But this interest extends (generically) to anything related to symplectic geometry and gauge theory.
My adviser is Michael Hutchings.

Notes & Papers

• An Exposition of Near-Symplectic Geometry (currently just a very rough sketch). A small note to help myself understand the subject and to give a talk on it.
• Introduction to Lagrangian-Intersection Floer Homology. A talk I gave in Denis Auroux's Fall 2011 seminar on Mirror Symmetry and Fukaya Categories.
• Seiberg-Witten Invariant and its (Physics) Relationship to Yang-Mills. A talk I gave in a Spring 2013 seminar. It describes the gauge theory of Electromagnetism and Yang-Mills-Higgs, the connections between vortices and monopoles and instantons, the topological applications of Seiberg-Witten theory, and its relationship to Donaldson's theory via supersymmetry.
• Essential Cohomology of the p-Groups with a Cyclic Subgroup of Index p. A paper I wrote as an undergraduate after learning Group Cohomology under my math mentor Ken Brown. The main bulk of the paper was a spectral sequence argument to compute a particular ideal in the cohomology ring of a particular group. It is currently only available on the arXiv.
• Solutions to "Cohomology of Groups". As an undergraduate I authored a solutions manual to Ken Brown's classic graduate textbook, as a good way to study the subject under his guidance. For now I am making it unavailable.

Non-math

String Theory requires the existence of extra spacial dimensions, and this could be the reason that gravity is weaker than the other three fundamental forces. At small distances Newton's Law of Gravitation should not just be an inverse-square proportion, but should have an exponential-decay perturbation (a Yukawa potential) which envelops the effects of these dimensions. Our experiment hopes to either detect this perturbation or extend the realm at which we know Newton's Law holds. This requires ultra-sensitive measurements, and as such it is run at extremely cold temperatures (using liquid Helium) and housed in a low-vibration floating room. My contribution was the design/construction of an apparatus to measure the gravitational force between two masses separated by a few microns.