## Abstract Convexity, Weak Epsilon-Nets, and Radon Number

Let F be a family of subsets over a domain X that is closed under taking intersections. Such structures are abundant in various fields of mathematics such as topology, algebra, analysis, and more. In this talk we will view these objects through the lens of *convexity*.

We will focus on an abstraction of the notion of *weak epsilon nets*:

given a distribution on the domain X and epsilon>0,

a weak epsilon net for F is a set of points that intersects any set in F with measure at least epsilon.

## Higher ribbon graphs

Ribbon graphs capture the topology of open Riemann surfaces in an elementary combinatorial form. One can hope this is the first step toward a general theory for open symplectic manifolds such as Stein manifolds. We will discuss progress toward such a higher dimensional theory (joint work with Alvarez-Gavela, Eliashberg, and Starkston), and in particular, what kind of topological spaces might generalize graphs. We will also discuss applications to the calculation of symplectic invariants.

## Math for underprivileged high school kids

We will hear from two passionate creators of successful mentoring programs in math for high school kids in educationally challenged environments. They will give back-to-back talks about their experiences and educational insights.

## Nodal domains for Maass forms

is expected to behave like a random monochromatic wave .

We will discuss this in connection with the question of the nodal

domains of such forms on arithmetic hyperbolic surfaces with a reflection symmetry .

( Joint work with A.Ghosh and A.Reznikov we will also discuss a recent result of

J.Jang and J.Jung ) .