Jacob Jonsson: Combinatorics and beyond the finite

Loosely speaking, combinatorics is the art of solving problems concerning finite or countable structures. This may seem to suggest that combinatorics is all about such "discrete" structures, but history has seen many successful applications of combinatorial methods to problems that are inherently "non-discrete". This talk pertains to simplicial complexes, which constitute a particularly useful bridge between combinatorics and other areas, including topology, geometry and algebra. Simplicial complexes admit several very different interpretations: as purely combinatorial objects, as  geometric objects in Euclidean space, and as monomial ideals in polynomial rings. The talk gives a few examples from the speaker's own research, illustrating how simplicial complexes (and perhaps some of their close relatives) show up in various settings.