“Counting curves using partial differential equations”
Giovedì 18 Giugno 2026, ore 14:30 - Aula 2BC30 - David Klompenhouwer (Padova, Dip. Mat.)
Abstract
Enumerative geometry is the art of counting geometric objects that satisfy certain geometric conditions. For example: how many plane curves, given by polynomials of degree d, pass through a fixed set of 3d-1 distinct points in the plane? These kinds of questions have been asked since ancient times. Partial differential equations (PDEs), on the other hand, are a much more recent tool and are used to model all sorts of physical phenomena. In the early 1990s, physicist Edward Witten made a striking conjecture that revealed an intimate connection between these two research areas. Since then, the love between enumerative geometry and PDEs has blossomed, giving rise to fascinating new insights in both areas.
In this seminar, I will give a friendly introduction to both of these topics, by focusing on objects and ideas that are of particular interest to me and showing how they are related. At the end, I will mention how my research attempts to explain this mysterious romance between enumerative geometry and PDEs.
The video of the seminar will appear shortly afterwards in this Mediaspace channel.
