Thematic Programme on Condensed Mathematics and p-adic Geometry

The fields of *condensed mathematics* and *p-adic geometry* have undergone rapid and transformative development over the past decade. Initiated by the foundational ideas of Clausen and Scholze, condensed mathematics provides a robust categorical framework for treating topological and analytic objects in an algebraic manner. This apparatus has become central not only to functional analysis, but also to arithmetic geometry, p-adic Hodge theory, the geometric Langlands program, and the emerging theory of analytic stacks.

Simultaneously, p-adic geometry, including advances in diamonds, perfectoid spaces, adic spaces, and prismatic cohomology, has reshaped our understanding of arithmetic structures and produced new approaches to old conjectures. The interaction between condensed mathematics and modern p-adic geometry has proven exceptionally fertile, providing conceptual clarity and powerful new tools for some of the most active research directions in number theory and algebraic geometry.

Despite these developments, exposure to these areas within India has so far been limited, and many early-career researchers are eager for sustained, systematic opportunities to learn and engage with these subjects. A dedicated thematic semester at the Lodha Mathematical Sciences Institute (LMSI) is therefore both timely and impactful. Bringing together international experts and Indian mathematicians will foster long-term collaborations, enhance the research ecosystem, and introduce advanced techniques that can influence multiple branches of mathematics in the country.

All participants are requested to click here to download and review the guidelines before applying.

For any questions, write to: contact@lmsi.org