Research
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 (and my work) on the abc-conjecture. This has led to my work on Arithmetic Teichmuller Spaces and the proof of the abc-conjecture which is available at arxiv.org. Frequently Asked Questions (FAQ) about the proof of the abc-conjecture.
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.
My reports on the Mochizuki-Scholze-Stix Controversy
- Final Report (May 2025) [Provides my final conclusion regarding the proof of the abc-conjecture.]
- Provisional Report (June 2024) [Written after extensive correspondence (in May-June 2024) with Peter Scholze and it provides robust conclusions regarding the invalidity of the Scholze-Stix Report, but because Mochizuki was objecting to my work (in March 2024),
I did not provide any conclusion on the proof of the abc-conjecture. This report also contains a time-line of events leading upto this report.]
My essays, guest blogpost and rebuttals written in this context
- November 2025: Letter to Peter Woit
- November 2025: FAQ about the proof of the abc-conjecture.
- April 2023: Mochizuki’s Corollary 3.12 and my quest for its proof
- November 2022: Guest blogpost explaining some aspects of my work on Arithmetic Teichmuller Spaces and its relationship with Mochizuki’s work for David M. Roberts’ Highergeometer blog.
- January 2022: Accessible comparison of my theory and Mochizuki’s theory
Links to my papers and essays on this topic are on the arxiv and also at nLab.