Dr. Alan Stapledon (Sydney Mathematical Research Institute)

Abstract
Many difficult problems in combinatorics have been solved by first finding a connection with algebraic geometry and then applying deep geometric ideas. For example, the problem of classifying the possible numbers of vertices, edges, triangles, etc. of a simplicial polytope was solved in this way, in one of the major achievements of combinatorics in the last century.
But what happens for more general combinatorial objects, where the connection with algebraic geometry breaks down? Remarkably, in many cases the ideas coming from geometry can be abstracted and applied even when the geometric spaces themselves no longer exist.
One striking example is the analogous problem for simplicial spheres, which remained open for over 50 years and was solved only recently using ideas of this kind. I will give a non-technical survey of some of these developments, both historical and modern.
15.10.2026, Zeit: 17:00, Raum G03-106