# Gergely Bérczi

Department of Mathematics,

Aarhus University,

Ny Munkegade 118, bldg. 1530,

DK-8000 Aarhus C, Denmark

Email: gergely.berczi@qgm.au.dk

I am an associate professor at Aarhus University and head of the Aarhus DFF Algebraic Geometry Group.

Before this, I spent 2 years at ETH Zürich in the group of Rahul Pandharipande and 9 years in Oxford working with Frances Kirwan. I obtained my PhD in 2008 under the supervision of András Szenes.

I am currently partially funded by AUFF Starting Grant 29289 and DFF Grant 40296.

Activities:

From January - June 2024, I am co-organising a semester at the Isaac Newton Institute Cambridge on New equivariant methods in algebraic and differential geometry. This includes a workshop on Singularity theory and hyperbolicity and a workshop on Moduli stack and enumerative geometry.

I co-organise the Algebraic Geometry Session of the 29th Nordic Congress of Mathematicians 3-7 July 2023 in Aalborg, Denmark.

I co-organise a Swissmap workshop Enumerative geometry of the Hilbert scheme of points at the SwissMAP Research Station in Les Diablerets in January 2024.

Preprints:

(with Jonas Svendsen) Fixed point distribution on Hilbert scheme of points, arXiv:2306.11521

We answer an old question by showing that all monomial ideals (i.e torus fixed points) on the punctual Hilbert scheme of points of the affine space A_k^n sit in the curvilinear component. This implies that the punctual Hilbert scheme is connected, which was only known for the full Hilbert scheme due to Hartshorne. We prove analogous results for the Quot scheme of points in higher rank.Tautological integrals on Hilbert scheme of points I. arXiv:2303.14807

Tautological integrals on Hilbert scheme of points II: Geometric subsets, arXiv:2303.14812

Tautological integrals on Hilbert scheme of points III: Applications, in preparation

We aim to develop a new method to study intersection theory of the Hilbert scheme of points on complex manifolds. The main result is an iterated residue formula for tautological integrals over the main component and certain geometric subsets with applications in classical enumerative geometry We also formulate a Chern-Segre-type positivity conjecture.Multiple-point residue formulas for holomorphic maps (with A. Szenes), arXiv:2112.15502

We develop a formula for the multipoint loci of holomorphic maps between complex manifolds, and prove a conjecture of Kazarian and Rimányi.Non-reductive geometric invariant theory and Thom polynomials, arXiv:2012.06425

We build a non-reductive GIT model for the Morin singularity locus of holomorphic maps, and develop a toric localisation formula for their Thom polynomials.