The Saint Louis Academy of Mathematical Sciences (SLAMS) will hold its third meeting on the evening of Friday, Nov. 18, in DuBourg Hall on the campus of Saint Louis University.

The speaker will be Stefan Steinerberger of the University of Washington. RSVP for dinner by Nov. 8.

## Revisiting the Idea of Boundary

A fundamental recurring principle in mathematics is that among all domains of fixed volume, the ball minimizes the surface area of the boundary (and this is one of the reasons why many things in nature are round). It's a fascinating story, and we'll show how it took almost 3,000 years and several good ideas to make this idea precise.

We will then revisit the idea of boundary: classically, it denotes the region between a set and its complement. However, when thinking about social networks or modern data science, there is the question of whether it is possible to define a notion of boundary more abstractly, say, on a combinatorial graph (where there is only the graph and no complement to speak of). If you look at the graph of social connections, for example, is there any sense in which your highly eccentric neighbor who actively avoids people is "on the boundary" as opposed to that other neighbor who is the soul of every party? Such notions do indeed exist, and they lead to rather pretty pictures as well as some tantalizing open problems. As happens frequently in mathematics, looking at things from a new angle will also tell us something new about the classical boundaries in good old Euclidean space.