Geometric properties of Hilbert schemes

August 24 to August 28, 2026

at the

American Institute of Mathematics, Pasadena, California

organized by

Ritvik Ramkumar and Gregory G. Smith

Original Announcement

This workshop 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:

  1. Identify which points on Hilbert schemes are smooth or have mild singularities.
  2. Clarify how the irreducible components of a Hilbert scheme fit together.
  3. Investigate Hilbert schemes of varieties beyond projective space, drawing on combinatorial and computational tools.

Material from the workshop

A list of participants.

The workshop schedule.