This federal Project Grant award, titled "CURVES, COMPLEXITY, AND CONFIGURATIONS", was granted by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program. The $278,000 award supports a 3-year research project at the University of Washington to investigate fundamental questions about the geometry and dynamics of surfaces, with applications in physics and materials science. The research has three main themes: developing a theory of Eisenstein series and cusp forms for the moduli space of translation surfaces, studying the relationship between combinatorial complexity and geometric length of saddle connections on translation surfaces, and exploring the general geometry and counting problems associated with configurations of curves and graphs on translation and hyperbolic surfaces. The research is expected to produce significant intellectual merit and broader impacts through engagement with students, commitment to diversity, and public outreach activities.
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