Webpage of Kirti Joshi

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 on the abc-conjecture. This has led to my work on Arithmetic Teichmuller Spaces which is available at arxiv.org.

My report (June 2024) on The status of the Scholze-Stix Report and an Analysis of the Mochizuki-Scholze-Stix Controversy.

Also see my (April 2023) essay Mochizuki's Corollary 3.12 and my quest for its proof.

In (November 2022) I wrote this guest blogpost explaining some aspects of my work on Arithmetic Teichmuller Spaces and its relationship with Mochizuki's work for David M. Roberts' blog. In (January 2022) I provided an accessible comparison of my theory and Mochizuki's theory in this article.

Links to my papers and essays on this topic are also at nLab.

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