Publications

Preprints

Teaching (Math313 Linear Algebra)

My research interests span a broad spectrum of problems in the fields of Algebraic Geometry and Number Theory. Some of my recent work is in the context of Shinichi Mochizuki's work on p-adic Teichmuller Theory and his work on the abc-conjecture. This has led to my work on Arithmetic Teichmuller Spaces which is available at arxiv.org. Recently I wrote a guest blogpost explaining some aspects of my work on Arithmetic Teichmuller Spaces for David M. Roberts' blog. Also see a more detailed and accessible discussion here.

Yasuhiro Wakabayashi's work establishing the generic case of my conjecture on dormant opers has appeared here (for opers of rank two) and here (for higher rank opers). This conjecture grew out of my work on Frobenius destabilized bundles and the Hitchin-Mochizuki morphism (joint with Christian Pauly) and Mochizuki's p-adic Teichmuller Theory