Hausdorff Summer School: The Circle Method - Entering its Second Century

The Circle Method emerged one hundred years ago from ideas of Ramanujan, Hardy and Littlewood, and quickly became the most powerful analytic method for counting solutions to Diophantine equations. As the Circle Method enters its second century, new work is making significant advances both in strengthening results in classical Diophantine settings, and in demonstrating applications in novel settings. This includes function field, number field, adelic, geometric, and harmonic analytic applications, with striking consequences in areas such as ergodic theory, subconvexity for L -functions, and the Langlands program. This summer school for graduate students and postdocs will present accessible lecture series that demonstrate how to apply the Circle Method in a wide variety of settings.