Gergely Bérczi 

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

From January 2025 I serve as the AI Chair for the EU Horizon university network Circle U. 

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:

• IMProofBench - An AI Benchmark for Mathematical Reasoning.   

• Since February 2025 I am a contributor of Project Numina.

• I also work on EpochAI's FrontierMath benchmark. Here’s a somewhat biased and overly enthusiastic article covering our Frontier Math weekend in Berkeley.

• I was an invited participant of the 2024 Mathematics and Machine Learning program at Harvard CMSA, Boston, and an invited speaker at the AMS Joint Math Meetings 2025 in Seattle, whose theme is Math&AI. 

• Since January 2025 I am the AI Chair for Aarhus University for the CircleU AI Knowledge Hub.

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

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

• I co-organised 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 Klüver) Reinforcement Learning the Chromatic Symmetric Function, arXiv:2410.19189
  Motivated by the Stanley-Stembridge positivity conjecture, we propose a conjectural counting formula for the coefficients of the chromatic symmetric function of unit interval graphs using reinforcement learning.

• (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. 

Recent talks

• Géométrie Algébrique et Géométrie Complexe 2024, CIRM Luminy
  A survey on non-reductive group actions and applications, Talk 1  , Talk 2 , Talk 3 

• Jean-Pierre Demailly Memorial Conference, Grenoble, 2024, Talk  

• GHiSP 2024, Levico Terme
  Tautological intersection theory of the Hilbert scheme of points, Talk  

• Mathematics and Machine Learning, Harvard CMSA, 2024, Short talk  
  A very informal summary of my recent Math&ML work, MLSummary