Xuwen Zhu

Sponsor: National Science Foundation

Microlocal analysis on special geometric structures

Many geometric spaces arising in mathematics and physics are not perfectly smooth — they contain singularities where the usual rules break down, and understanding their structure is a central problem in differential geometry. This project develops new analytic techniques for a class of singular spaces tied to gauge theory, string theory, and the mathematical description of electromagnetic systems, advancing fundamental geometry while illuminating questions in theoretical physics.