Positive and Mixed Characteristic Birational Geometry and its Connections with Commutative Algebra and Arithmetic Geometry

Algebraic geometry is an important field of mathematics whose goal is to understand fundamental geometric shapes called algebraic varieties. The study of such shapes is a source of many applications, for example, in cryptography, engineering, or biology. The principal investigator's research centers around algebraic varieties and singularities in arithmetic settings. The PI plans to expand and build upon recent breakthroughs in arithmetic and complex geometry to increase our understanding of such objects. The PI will involve graduate students in this research and organize workshops aimed at early career mathematicians.

The key goal of the PI is to develop and apply new techniques related to Hodge theory, p-adic Riemann-Hilbert correspondence, and quasi-F-splittings to describe the behavior of higher differential forms in positive characteristic, improve our understanding of mixed characteristic singularities, and extend the validity of the Minimal Model Program in the arithmetic settings. This work will lead to new advancements in birational geometry and commutative algebra.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Award Number: 2602580
Principal Investigator: Jakub Witaszek
Funds Obligated: $183,022
State: IL