Stable Homotopy Theory and Arithmetic Geometry

Dates: Feb 15–May 15, 2027

Location: Harvard CMSA, 20 Garden St, Cambridge MA

This program will focus on interactions between stable homotopy theory and arithmetic geometry. In recent years, ideas from homotopy theory have begun to play an important role in areas such as $p$-adic cohomology, prismatic methods, and aspects of the Langlands program, while techniques from arithmetic geometry have led to new insights and computations in chromatic homotopy theory. Despite this growing overlap, researchers in the two areas often use different languages and tools. A central goal of the program is to make these ideas more accessible across fields and to encourage collaborations around shared problems.

The program will run from February 15 to May 15 and will be built around research and informal collaboration. It will begin with a short introductory bootcamp, followed by two focused workshops (one near the start and one toward the end), a weekly seminar with broadly accessible talks, and a weekly open-problem session. Most of the time will be left open for discussion and joint work among participants, aiming to spark new projects and longer-term connections between the two communities.

The program will include:

(1) a bootcamp during the first week, consisting of introductory lectures on both subjects;
(2) two research workshops—one during the second week and one near the end of the program—
highlighting current developments, especially those at the interface of the two areas;
(3) a weekly seminar featuring talks of broad relevance to participants; and
(4) a weekly open-problem seminar aimed at proposing and developing collaborative research directions, both for the duration of the program and beyond.

Organizers: Tomer Schlank (UChicago), Jared Weinstein (BU), Mark Kisin (Harvard), Jeremy Hahn (MIT), Lucas Mann (Münster)