Virtual invariants on the nested Hilbert scheme of points

During his studies, Felix has explored the nested Hilbert scheme of points, a moduli space parametrizing fundamental objects and therefore relevant in many fields of mathematics, physics and computer science. Felix has embedded this into smooth moduli spaces to better understand its mysterious geometry. 

This has led to a new description of known invariants for the Hilbert scheme of points on a complex two-space and a proof of a closed formula for these. It has also led to new invariants for the nested Hilbert scheme of points on a complex hyperspace of any dimension. An effective formula for the calculation of this has been derived, and it is hoped that these invariants can eventually be linked to known invariants in dimensions 2, 3 and 4.

The PhD study was completed at Department of Mathematics, Faculty of Natural Sciences, Aarhus University.

This summary was prepared by the PhD student.

Time: Thursday 8 October 2026 at 14:15.
Place: Building 1531, room 119, Auditorium D2, Deptartment of Mathematics, Aarhus University, Ny Munkegade 116, 8000 Aarhus C
Title of PhD thesis: Enumerative Geometry on the Nested Hilbert Scheme of Points via Moduli of Weak Algebraic Structures
Contact information: Felix Minddal, e-mail: femi@math.au.dk, tel.: +45 29648097
Members of the assessment committee:
Professor Fabien Pazuki, Department of Mathematics, Copenhagen University, Denmark
Professor Joachim Jelisiejew, Department of Mathematics, University of Warsaw, Poland
Professor Cristiano Spotti (chair), Department of Mathematics, Aarhus University, Denmark
Main supervisor: Associate Professor Gergely Bérczi, Department of Mathematics, Aarhus University, Denmark
Language: The PhD dissertation will be defended in English

The defence is public.
The PhD thesis is available for reading at the Graduate School of Natural Sciences/GSNS, Ny Munkegade 120, building 1521, 8000 Aarhus C