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Below are listed the available research areas. Note that the list may be updated up until the application deadlines.

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Earliest starting date: **1 September 2023**

The DFF Aarhus Algebraic Geometry Group's research profile lies in algebraic geometry, algebraic topology and symplectic geometry with applications in global singularity theory, complex geometry and enumerative geometry. The main themes we work on are:

- Equivariant techniques to study (non-reductive) group actions, topology and intersection theory of moduli spaces.
- Hyperbolic varieties, the Kobayashi and Green-Griffiths-Lang hyperbolicity conjectures
- Enumerative geometry: Hilbert scheme of points, Multisingularity classes of maps
- K-stability and K-moduli spaces
- DeepMath: using machine learning (deep NN's and reinforcdement learning) approach in geometry
- Algebraic statistics

**Keywords:** Algebraic geometry, algebraic topology, global singularity theory, hyperbolicity

Funding agency: **Independent Research Fund Denmark (DFF)**

Duration: **24 months**

Host: **Gergely Berczi**

Preferred start date: **1 September 2023**

Project description: We seek a postdoc interested in building on recent advances in analytic number theory, automorphic forms, representation theory or some combination of these topics.

The analytic theory of automorphic forms and L-functions is a central part of modern number theory. The field is characterized by problems rather than methods. A central problem is to provide nontrivial estimates for L-functions; despite some progress, a solution remains elusive. Some recent work by the PI has involved techniques coming from representation theory and microlocal analysis, among other sources.

Funding agency: **Start package**

Expected duration: **24 months with the possibility of extension by 12 months**

Host: **Paul Nelson**

Preferred start date: **1 March 2023**

Recent research has shown that living cells react in a very refined manner to mechanical forces exchanged with their surroundings. This makes it relevant to ask: how do cells react to variations in the microstructural geometry of their environment?

This interdisciplinary project shall devise tools to clarify this question through experimental and mathematical modelling. To this end, we will combine and develop approaches from Mechanobiology, Materials Science, Stereology/Image Analysis and Stochastic Geometry.

The project is carried out jointly with Jens Vinge Nygaard's research group at the Department of Biological and Chemical Engineering. You will work on mathematical aspects - the project offers some flexibility to set your own focus, depending on your research interests. Read more under https://mechanogeometry.au.dk

Funding agency: **Villum Foundation**

Expected duration of position: **24 months**

Host: **Ute Hahn**

Preferred start date: **1 August 2023**

The area of the postdoc is complex differential geometry with an emphasis on the study of special Hermitian metrics. More precisely, the current postdoc will focus on the investigation of analytic and cohomological properties of compact complex manifolds that carry such metrics and the extent to which celebrated results in Kähler geometry generalize to this broader setting. The project will also make use of tools from adjacent fields such algebraic topology, toric geometry and number theory.

Funding agency: **Villum Foundation**

Duration: **12 months**

Host: **Alexandra-Iulia Otiman**

Preferred start date: **1 August 2023**.

We look for a postdoc interested in investigating interactions between differential and algebraic geometry, with special emphasis on the study of the collapsing of canonical geometries (Calabi-Yau, negative Kähler-Einstein, constant scalar curvature, etc…) and algebro-geometric degenerations in relation to moduli problems for higher dimensional complex varieties. Furthermore, possible applications to nearby areas (e.g., Arakelov Geometry) will be considered.

These themes, at the cutting edge of the latest developments in Kähler geometry, are highly interdisciplinary requiring techniques ranging from geometric PDEs to more algebro-geometric tools, thus we expect candidates to have a good expertise in some of these areas.

Funding agency: **MATH**

Duration: **24 months**

Host: **Cristiano Spotti**

Preferred start date: **1 June 2023**

Calabi-Yau categories are key objects of modern mathematics. The goal of this project is to find invariants of Calabi-Yau categories, compute their symmetries, and to classify them. We expect this to be part of a wider range of activities within homological algebra, which may include one or more of the following areas: Auslander-Reiten theory, Differential Graded categories, extriangulated categories, higher homological algebra, singularity categories.

Funding agency: **DNRF, the Danish National Research Foundation**

Expected duration of position: **12 months**

Host: **Peter Jørgensen**