Math work
Mathematics
A couple math things that I have been stewing over:
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Calculating the explicit image of of a $\mathcal D$-module on $\mathbb A^1$ in the Sato Grassmannian under the Cannings-Holland correspondence.
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Realizing the Lax matrix for the 2D double elliptic integrable system as a Higgs field for something like an "elliptic Hitchin system".
Projects nearer to completion will have preprints available. Unavailable preprints can be made available upon request.
My Papers
Some of my old papers on the arXiv:
Spectral Description of the Spin Ruijsenaars-Schneider System
In this paper I show that the classical spin Ruijsenaars-Schneider phase space can be given a moduli-theoretic interpretation in terms of twisted Higgs fields on cubic curves. The moduli-theoretic interpretation provides a completion for this phase space, and the RS flows are identified with the natural flows that exist on twisted Hitchin systems of this kind.
Langlands parameters of quivers in the Sato Grassmannian
In this paper, Martin Luu and I show that associated to the combinatorial data of a quiver in the Sato Grassmannian, one can construct a "local Langlands parameter" on $\mathbb A^1$. In fact, there are a number of different ways of constructing this local Langlands parameter, and we prove some equivalences between them.
Old Notes
Some notes on the class field theory. These are lecture notes I prepared for a seminar on the Langlands program. The hope is that I will find the time to continue preparing these notes, and eventually touch on subjects like Tate's thesis, geometric class field theory, and finally the Langlands program.