The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

The minimum spanning tree of 100,000 uniformly random points. Colors encode graph distance from the root, which is red. Black points are those whose removal would disconnect at least 5% of the points from the rest.

This program is devoted to the study of the probabilistic and statistical properties of such networks. Central tools include graphon theory for dense graphs, local weak convergence for sparse graphs, and scaling limits for the critical behavior of graphs or stochastic processes on them. The program is aimed at pure and applied mathematicians interested in network problems.

Extremal combinatorics concerns itself with problems about how large or small a finite collection of objects can be while satisfying certain conditions. Questions of this type arise naturally across mathematics, so this area has close connections and interactions with a broad array of other fields, including number theory, group theory, model theory, probability, statistical physics, optimization, and theoretical computer science.

Activist Bob Moses argued that mathematical literacy was the next civil rights front line. The 2025 CIME workshop will explore what mathematical literacy might mean and why it still matters for citizenship now and in the future. The workshop’s long-term impact relies on the participation of research mathematicians, mathematics educators, educational researchers, teachers of school mathematics, and policymakers working across different perspectives and roles to foster collaboration that will raise the floor for mathematical literacy for citizenship now and in the future.