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.

In recent years techniques from harmonic analysis viz. projection theorems have found striking applications in finitary analysis on homogenous spaces. Such quantitative results have many potential applications to analytic number theory. This workshop will bring together researchers in these areas to further explore these connections.

This research conference will feature plenary talks by leading researchers, career panels, professional development opportunities, and scientific sessions in the following areas: (1) Algebra/Number Theory, (2) Combinatorics, (3) Harmonic Analysis, PDEs & Differential Geometry, (4) Numerical Analysis and Computational Mathematics, (5) Machine Learning, (6) Mathematical Biology, (7) Statistics, Data Analysis, and (8) Math Education.

The goal of the conference is to encourage attendees to pursue careers in the mathematical sciences, to showcase research being conducted at the forefront of their fields, and, finally, to build a community around shared academic interests. The conference will be held on the UCLA campus in Los Angeles, CA.

LatMath is funded by the National Science Foundation Division of Mathematical Sciences, with additional support from generous sponsors.