David Gay (U. Georgia and MPIM Bonn): Two-dimensional shadows of four-dimensional topology

Visualizing four-dimensional topology is notoriously challenging; even three dimensions can be more challenging than you might think. In the end, if we want to communicate ideas on paper (or on a screen) and make rigorous arguments, we seem to need to reduce things to dimension two, i.e. draw a picture or cast a shadow onto a two-dimensional surface. I'll discuss some new fun ways to draw 2-dimensional diagrams of closed (compact and without boundary) 4-dimensional spaces and embedded objects inside such spaces, coming from trisections of these spaces, i.e. decompositions into three identical pieces. Along the way I'll present an algebraic question about triples of square integer-entry matrices.