for this workshop
Geometric properties of Hilbert schemes
at the
American Institute of Mathematics, Pasadena, California
organized by
Ritvik Ramkumar and Gregory G. Smith
This workshop, sponsored by AIM and the NSF, will focus on the geometry of Hilbert schemes. Despite their importance, many of their geometric properties remain mysterious. Classically, the Hilbert scheme of projective space was shown to be path-connected, while the Hilbert scheme of points on a smooth curve or surface is smooth. Beyond these foundational results, most research has centred on constructing pathological examples of Hilbert schemes that parametrize curves and higher-dimensional objects, revealing a striking contrast between the well-behaved and pathological cases. Recent breakthroughs have uncovered new smooth components of Hilbert schemes, identified extreme singularities, and exposed unexpected connections to combinatorics and linkage theory. This workshop will bring together experts and early-career researchers from around the world to advance our understanding of Hilbert schemes.
The goals of the workshop are:
- Identify which points on Hilbert schemes are smooth or have mild singularities.
- Clarify how the irreducible components of a Hilbert scheme fit together.
- Investigate Hilbert schemes of varieties beyond projective space, drawing on combinatorial and computational tools.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than March 24, 2026.
Before submitting an application, please read the description of the AIM style of workshop.
For more information email workshops@aimath.org
