Project Grant 2153758

The National Science Foundation Division of Mathematical Sciences awarded a $275,000 Project Grant to the University of California, Los Angeles under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The three-year award will support research into fields in tensor-triangular geometry and their applications. Specifically, the awardee will analyze fundamental particles in tensor-triangular geometry known as tensor-triangular fields, which underlie larger tensor-triangulated categories. The research aims to develop techniques to construct such fields in representation theory and motivic theory where candidates are not yet known. It also provides training for graduate students. Insights from understanding tensor-triangular fields are expected to generate applications throughout tensor-triangular geometry similar to how fields define ranks and counts in algebraic geometry.