Forskningsprojekter

Aarhus Diophantine Approximation

Aarhus Diophantine Approximation is a group of researchers working in Diophantine approximation. We have interests in irrationality and transcendence of numbers which are given by their expansions as infinite series, infinite products or continued fractions. In addition, we have a strong interest in the metric theory of Diophantine approximation.

PI: Simon Kristensen

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Limits of geometries over the p-adic numbers

At the root of scientific evolution, classifying all possible geometries of a given object and exploring all possible transitions between them are crucial. Often, geometries are modeled over our usual number system, the real numbers. Instead, my research project will focus on geometries modeled over the p-adic numbers, where p is a prime number and the digits used are from 0 to p−1. The objective is to answer the following fundamental questions for many of the possible p-adic geometries: Given a family of geometries, can one compute all its possible limits of geometries? Can one provide precise geometric transitions towards those limits?

PI: Corina-Gabriela Ciobotaru

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Complex Calderón Problem

The project is on inverse coefficient problems in connection with applied analysis and PDEs. In particular reconstructing an interior conductivity coefficient in Calderón's inverse problem, based on boundary electrical measurements in the form of a Neumann-to-Dirichlet mapping. A related problem is to determine the support of unknown conductivity-perturbations using e.g. monotonicity and localization for quadratic forms.

PI: Henrik Garde

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Aarhus Operator Algebra Group

The project is concerned with studying both the ideal structure of C*-algebras and the structure of KMS states on C*-algebras. The center of attention of the project is the C*-algebras arising from groupoids, where the structure of both ideals and KMS states is often closely connected to certain underlying groups of the groupoids. The project’s main aim is to utilize these connections to answer fundamental questions regarding ideal structure of C*-algebras, KMS states and groupoid C*-algebras.

PI: Johannes Christensen

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MechanoGeometry - how do cells react to geometric properties of their environment?

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?

PIs: Ute Hahn and Jens Vinge Nygaard (BCE)

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Energy Lives! Infrastructural Citizenship in Nordic Energy Transitions

The world is in dire need of societal and technological pathways that go beyond our current dependency on fossil fuels. The Nordic countries are committed to green transitions towards low-carbon societies, largely centered on renewable energy sources and electrification of society. Because energy transitions are complex multilayered historical processes, looking to historical energy transitions for guidance can help the Nordic countries develop new energy systems that are environmentally and socially just.

PIs: Matthias Heymann et al

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Categories, Clusters and Completions

This covers two subprojects: (1) Cluster algebras and invariants and (2) Metrics and completions of triangulated categories

PI: Sira Helena Gratz

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Canonical Metrics in Complex Geometry

Canonical metrics in Complex Geometry are a fundamental tool to study complex manifolds. Our Villum funded research activities are based on projects focused on the study of such metrics in the Kähler case (which include the famous Käher-Einstein metrics), as well as in the non-Kähler case, where most of even the basic problems remain quite mysterious. In particular, we combine tools ranging from algebraic geometric to geometric analysis to understand the formation of singularities, degenerations and collapsing of such canonical metrics. This is related to the constructions of moduli compactifications for spaces of complex varieties.

PI: Cristiano Spotti

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Conformal Geometry: Metrics and cohomology

This project meant to explore complex manifolds admitting special geometric structures, with the ultimate purpose of obtaining suitable and strong classification criteria. Locally conformally Kähler (lcK) manifolds represent a key link between conformal and Kähler geometry and play an important role in understanding the properties of complex manifolds of non- Kähler type. We endeavour through this project to investigate on lcK manifolds fundamental problems of modern geometry such as cohomological obstructions to the existence of special metrics, classification and compatibility between different structures.

PI: Alexandra-Iulia Otiman

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Applied Statistics Laboratory

The Applied Statistics Laboratory (aStatLab) is a research group that works parallel to the theoretical statistics and the probability research groups at the Department of Mathematics, Aarhus University (AU). The aStatLab aims to research applied statistics, including developing new methods in statistics inspired by real applications. Several research groups at AU and external partners collaborate with and receive statistical support from the aStatLab.

PI: Rodrigo Labouriau

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Matrix-analytical methods in population genetics

Understanding the impact of global climate change and implementation of management resources for threatened populations requires detailed knowledge of the genetic and demographic history of these populations. Genetic polymorphism data represent a major resource of information, but the present methods are often limited to large spatial and temporal scales of limited practical interest

PI: Asger Hobolth

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Towards sustainability of global resources, fair trade and global justice?

Climate change, rising resource competition and global inequality pose tremendous challenges to contemporary societies around the globe and urgently require fundamental processes of transformation to sustainable practices and global justice. Historical research contributes valuable knowledge about the complexities, conflicts and impediments of such transformation as well as experiences of successful cases and best practices. The problem fields in question – sustainable development, resource security and global justice – are closely linked, but research mostly neglects these links. In addition, perspectives of the Global South and the Global North need to be negotiated and developed together.

PI: Matthias Heymann

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Aarhus Algebraic Geometry Group

The Aarhus DFF Algebraic Geometry Research group is based at the Department of Mathematics of Aarhus University. Our research interest is at the interface of algebraic geometry, algebraic topology and symplectic geometry with applications in global singularity theory, complex geometry and enumerative geometry.

PI: Gergely Bérczi

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Aarhus Automorphic Forms

The project concern researchs in analytic number theory, automorphic forms and/or representation theory, building on recent advances in these subjects. 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.

PI: Paul D. Nelson

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Special metrics in Kähler geometry

Our main aim is to find effective (geometric) criteria for solvability of these infinite families of geometric PDE. This is motivated by finding finitely many optimal destabilizing subvarieties to numerical criteria (or in the longer perspective, optimal destabilizing test configurations to e.g. K-stability), and also has direct implications for proving existence of wall-chamber type decompositions for geometric PDE.

PI: Zakarias Sjöström Dyrefelt

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Phase Transitions for the Boolean Satisfaction Problem

Artificial intelligence (AI) is concerned with enabling machines to make "intelligent choices". In AI planning, the branch of artificial intelligence involving intelligent agents, autonomous robots, and crewless vehicles, the "intelligent choices" are based on finding a strategy based on a description of the world, the desired goals, and the possible actions to achieve the given goals. Finding these strategies is a very complex problem.

PI: Andreas Basse-O'Connor

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Can Active Colloids Have Collective Behavior?

Nanobots, propelled by converting energy sources into kinetic energy, surpass Brownian motion but face challenges due to gaps in fundamental understanding and a lack of design predictability, resulting in low-energy and less controllable nanobots. Our hypothesis suggests that interparticle forces play a crucial role in enabling collective motion in a nanobot ensemble.

PIs: Brigitte Maria Städler (iNano) and Christian Pascal Hirsch

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Towards Responsible Explainable AI Technologies

Towards Responsible Explainable AI Technologies (TREAT) examines advantages and disadvantages of so-called “Explainable AI” technologies for creating and using AI in an ethically responsible manner. One of the main ethical concerns regarding the use of complex AI systems in high-stakes decision making is that they risk become unintelligible black boxes. In response, a new subfield within AI research, known as explainable AI (XAI), seeks to develop tools for generating explanations of AI systems. Such explanations are important in order to enable people to understand and thereby think critically about the AI systems that are increasingly impacting our everyday lives. However, explanations are not just an ethical good. They also risk creating a false sense of understanding, which can be exploited to mislead or even manipulate.

PI: Rune Nyrup

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Revideret 13.11.2025

Lars Madsen