Arizona Winter School research community

Arizona Winter School research community

This research community, sponsored by AIM and the NSF, is a virtual companion to the Arizona Winter School, centered around two short courses each Fall aimed at advanced undergraduate and beginning graduate students broadly interested in Number Theory.

There are two main goals to this program:

• To engage students with a broad spectrum of academic preparation and backgrounds in number theory and encourage future engagement; and
• To increase the preparedness of students for graduate studies in Number Theory and the in-person Arizona Winter School.

This program will take place across nine weeks in Fall 2025 and 2026, anchored by two short virtual courses around which we will build a vibrant online community of students and teaching assistants.

The 2026 Arizona Winter School topic is "Computational Aspects of Arithmetic Geometry and Cryptography." Accordingly, the Fall 2025 preliminary school will feature courses around mathematical cryptography and the analysis of algorithms in Number Theory. The first course will be aimed at advanced undergraduates, and only a first course in abstract algebra will be assumed as a prerequisite. The second course will be more advanced and assume more background in number theory, though it will not assume fluency in the analysis of algorithms.

Applications to participate are welcome. More details, including the application to participate in the Preliminary Arizona Winter School, are available on the Arizona Winter School website.

Each short course interleaves asynchronous lectures and problem set discussions in alternate weeks. Based on extensive, tailored course notes prepared before the school, each course leader records five asynchronous lectures, released every two weeks starting in late September. After each lecture, an accompanying problem set is released. Students accepted to the virtual school are paired with teaching assistants — typically late-stage graduate students or postdocs — in small discussion groups to review the course material and the problem sets during off-lecture weeks. Community events exposing students to professional resources, e.g., a panel on "Graduate School Applications," are sprinkled throughout the nine weeks of the school.

Lecture notes, recordings of talks, problem sets, and other information are dynamically posted during the school and permanently archived at the Arizona Winter School website.

Apply to participate in this research community. Applications are open to everyone.

For more information email research@aimath.org