<p>A wall-crossing in a moduli problem</p>

One of the central problems in algebraic geometry is to classify so-called algebraic varieties: geometric shapes cut out by polynomial equations. Algebraic varieties are parametrized by certain moduli spaces (roughly: parameter spaces whose points correspond to these different varieties). The geometry of these moduli spaces encodes the ways of continuously deforming these shapes. Furthermore, classification questions for algebraic varieties often boil down to understanding the geometry of these moduli spaces. In the past few years, powerful new tools have been developed in moduli theory, especially for higher dimensional varieties – those which are of complex dimension at least two. The goal of this summer school is to provide an introduction to many of these recently emerging breakthroughs to enable graduate students to begin working in this area. The program will be motivated and often guided by examples and is intended to be accessible to a wide variety of students

The Simons Laufer Mathematical Sciences Institute (SLMath) will host the 2026 Modern Math Workshop (MMW) as part of the SACNAS Annual Conference. The Modern Math Workshop encourages undergraduates to pursue careers in the mathematical sciences, and builds research and networking opportunities among undergraduates, graduate students and recent PhDs in the mathematical sciences.

The goal of our school is to make connections between different flavors of geometry: euclidean geometry, hyperbolic geometry, translation surfaces and graph theory. We will focus on growth, asymptotics and extremal problems.

Scheduled at ICARM in Pittsburgh, Computer-Aided Reasoning for Algebraic Geometry is a summer school designed for 40–50 graduate students and junior researchers. This workshop positions algebraic geometry, formalization, and artificial intelligence as the three vertices of a connected framework, bridging the gaps between these distinct skill sets. Participants will explore topics beyond standard introductory courses through a rigorous schedule of blackboard-style foundations lectures, Lean formalization sessions, and hands-on machine learning tutorials. The program features a heavy emphasis on collaborative afternoon group projects led by expert mentors, allowing students to apply state-of-the-art autoformalization tools and ML pipelines directly to open problems in algebraic geometry.

The PIMS–CRM Summer Schools in Probability are a highlight of Canadian probability. Launched by PIMS in 2004, they take the form of two main 4-week courses by top researchers in probability theory and related fields, along with a number of keynote addresses and shorter mini-courses. The school is geared primarily at doctoral students and postdoctoral scholars, who are also given the opportunity to present their own research, should they desire. The schools have played a major role in the development of an exceptionally strong community of young probabilists in Canada, North America and overseas. This will be the 14th time this school has run. 

The Whitney Umbrella. Courtesy of Herwig Hauser, Fac. Math., University of Vienna, Austria

The school will introduce students to the fundamental problem of resolution of singularities of varieties and schemes. This is a subject that is relevant for all areas of algebraic geometry and commutative algebra. Students will learn algorithms to resolve singularities, and learn how to apply them in specific situations and understand how these techniques can be used in their research.