Coffee and snacks will be provided. This talk will be recorded for later viewing.

Abstract: In this talk, I will explore the interesting geometries that emerge in high-dimensional attraction basins, which are important in applications such as protein folding, cell differentiation, and neural networks. Using simple networks of coupled oscillators, I will show that high-dimensional basins are generally highly nonconvex and nonlocal, with most of the basin volume concentrated in tentacle-like structures. Next, I will show that introducing non-pairwise interactions in the network can make basins deeper but smaller—the attractors become linearly more stable but much harder to find due to basins shrinking dramatically. I will end with a few applications to neuroscience.