Institute of Algebraic Geometry, Leibniz University Hannover

Emmy Noether Junior Research Group: "Smoothings from log resolutions and applications"

• Tim Gräfnitz — Principal Investigator
• Alejandro Ovalle — PhD Student

Winter Semester 2026/27: Toric Geometry

Lecture: Thursdays, 10:15–11:45 (starting October 15)
Building 3110, Room 016

Exercise Class: Thursdays, 9:15–10:00 (starting October 22)
Building 3110, Room 016

In the first lectures, I will mostly follow Simon Telen's lecture notes, which are based on the book Toric Varieties by Cox, Little and Schenck. Later, we will cover more specialized topics in toric geometry.

Exercise Sheets

will appear here

Research Interests

• Algebraic Geometry
• Logarithmic Geometry
• Tropical Geometry
• Enumerative Geometry
• Mirror Symmetry
• Deformation Theory

Publications and Preprints

• Smoothings from zero mutable Laurent polynomials via log resolutions and divisorial extractions
  Preprint, 2025, to appear in Mathematische Zeitschrift.
  arXiv:2503.18661
• Singular Log Structures and Log Crepant Log Resolutions I
  With Alessio Corti and Helge Ruddat. Preprint, 2025.
  arXiv:2503.11610
• Enumerative geometry of quantum periods
  With Helge Ruddat, Eric Zaslow and Benjamin Zhou. Advances in Mathematics 499, 111063.
  arXiv:2502.19408
• Gromov-Witten invariants and mirror symmetry for non-Fano varieties using scattering diagrams
  With Per Berglund and Michael Lathwood. Preprint, 2024.
  arXiv:2404.16782
• The dense region in scattering diagrams
  With Patrick Luo. Bulletin of the Australian Mathematical Society 109 (2025), 1–13.
  arXiv:2312.13990
• Counting (tropical) curves via scattering.sage
  Preprint, 2022.
  arXiv:2210.10455
• The proper Landau-Ginzburg potential is the open mirror map
  With Helge Ruddat and Eric Zaslow. Advances in Mathematics 447 (2024), 109639.
  arXiv:2204.12249
• Theta functions, broken lines and 2-marked log Gromov-Witten invariants
  Manuscripta Mathematica 176 (2025), 41–76.
  arXiv:2204.12257
• Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs
  Journal of Algebraic Geometry 31 (2022), 687–749.
  arXiv:2005.14018

Theses

• Doctoral thesis
  Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs, 2020.
• Master thesis
  Tropicalization of the lines on the Dwork pencil of quintic threefolds, 2017.

• scattering.sage
  Computing scattering diagrams and wall structures in the Gross–Siebert program.
• mutation.sage
  Computing mutation graphs of zero mutable Laurent polynomials.
• tomjerry.sage
  Computing dual pairs of zero mutable Laurent polynomials on rectangular triangles.

• 2026– Emmy Noether Research Group Leader, Leibniz University Hannover
• 2023–2026 Postdoctoral Researcher, Leibniz University Hannover
• 2022–2023 Postdoctoral Researcher, University of Cambridge
• 2021–2022 Postdoctoral Researcher, Ruhr University Bochum
• 2017–2021 PhD in Mathematics, University of Hamburg

Email:
graefnitz@math.uni-hannover.de
Address:
Institute for Algebraic Geometry
Leibniz University Hannover
Welfengarten 1, 30167 Hannover, Germany
Room d401