This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $113,376 to Brown University to develop techniques for understanding the geometry of solutions to systems of polynomial equations. The research focuses on three main areas: 1) the natural stratification of the space of vector bundles on a curve, 2) the interpolation problem in other settings like homogeneous spaces, and 3) the rationality problem for varieties over non-closed ground fields. The award period runs from Sep 1, 2024 to Aug 31, 2029 and will be complemented by educational and outreach activities, including workshops for early-to-mid career women and non-binary graduate students in algebraic geometry and undergraduate research mentoring.
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