With support from this award, the Southwest Center for Arithmetic Geometry will continue its series of annual "Winter Schools" in 2016, 2017, 2018, with the 2016 Arizona Winter School taking place March 11-16, 2016 at the University of Arizona in Tucson, AZ. Since its founding in 1997, the primary activity of the Southwest Center is the Arizona Winter School (AWS), an annual meeting which has become a prominent national event and provides high-level training and research experience for graduate students in arithmetic geometry and related areas. The AWS is an intensive five-day meeting, organized around a different central topic each year, that features a set of courses and accompanying research projects carefully designed and delivered by leading and emerging experts. At the Winter School, connections among peers are formed, and mentoring relationships between students and senior researchers are developed. As has been the case at previous Winter Schools, subsequent collaborations between participants at all levels are the norm. Students make concrete strides toward becoming research mathematicians, post-doctoral assistants gain valuable mentoring experience in their academic careers, and faculty develop new interests and see new connections that lead to important published results. The Southwest Center website shares reusable content from the Winter Schools, including lecture notes, project descriptions, and audio and video of lectures. Through these thorough records, the dialogues begun at the AWS are extended to the greater community, and the efforts of the AWS participants are made freely and indefinitely available to all.
The AWS is a unique fusion of traditional mathematics conference and intensive research workshop: the speakers organize courses of four lectures, provide lecture notes in advance, and propose research projects for graduate students to work on during the meeting. Nightly working sessions on these projects and on separate problem sets are run by the speakers and postdoctoral fellows. On the last day, students present their findings to the participants of the meeting. The result is a particularly intense and focused five days of mathematical activity for everyone involved. Recent Winter School topics have included "Modular forms and modular curves", "Arithmetic statistics", and "Arithmetic and higher dimensional varieties." The topics of upcoming Winter Schools will be guided by future mathematical developments. More information about the upcoming and past Arizona Winter School programs can be found at the Southwest Center's website: http://swc.math.arizona.edu/