This award funded research on determining when systems of polynomial equations have solutions where all of the coordinates are rational numbers (i.e. fractions). By work of Manin in the 1970's, an integral component of this problem is understanding the so-called Brauer group of the system (or variety). Our current approaches naturally partition the Brauer group into two parts: the algebraic part and the transcendental part. Historically, our knowledge of the transcendental part has lagged far behind our knowledge of the algebraic part. As a result of this award, our knowledge of the transcendental part has dramatically increased. We now have the tools to compute the transcendental part of the Brauer group for any Enriques surface, as well as a large number of transcendental elements for cyclic covers of P^2. Both of these cases are fundamental examples and will inform further breakthroughs. Surprisingly, this research direction also provided new advances in the understanding of the algebraic part of the Brauer group for some key examples. All results funded from this award were made publicly available. The resulting publications are posted on arxiv.org, as well as on the PI's website. Numerous talks on these results were also given, disseminating the work to a broader audience.
