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Research areas open for postdoc applications with deadline 1. August 2021

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

Tip: you can collapse an area box by clicking the circled "-".

(PD-1) Spatial Random Networks and Topological Data Analysis

Preferred start date: 1 January or 1 February 2022

Project area: Spatial Random Networks and Topological Data Analysis

The aim of this project is the development of asymptotic results for spatial random networks and for topological data analysis on large random structures. This includes for instance the investigation of novel forms of continuum percolation that can capture higher-order interaction. Moreover, limit results such as the law of large numbers, the central limit theorem, and large deviations theory provide the foundation for basic statistical properties such as consistency and asymptotic normality. This is of high relevance since the statistical foundations of topological data analysis are still in its infancy.

Funding agency: Aarhus University's Strategic Digitalization Initiative

Expected duration of position: 36 months

Host: Assoc. Prof. Christian Hirsch

(PD-2) Calabi-Yau categories

Preferred start date:  1 January 2022

Project area:  Calabi-Yau categories

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.

Funding agency: DNRF, the Danish National Research Foundation

Expected duration of position:  24 months

Host: DNRF Chair, Prof. Peter Jørgensen

(PD-3) Higher dimensional cluster theory

Preferred start date:  1 January 2022

Project area:  Higher dimensional cluster theory

Classic cluster theory is controlled by two-dimensional combinatorial structures like triangulations of surfaces.  This project aims to generalise cluster theory to higher dimensions, with the key aim of defining higher dimensional cluster algebras.  The methodology builds on known examples of higher dimensional cluster categories and tropical friezes.

Funding agency: IRFD, Independent Research Fund Denmark

Expected duration of position:  36 months

Constraint: Applicants for this project must have obtained their PhD degree after 1 August 2017. In case of maternity/paternity leave taken after obtaining the PhD, subtract 2 times the months of leave from the above date.

Host: DNRF Chair, Prof. Peter Jørgensen

(PD-4) Gromov-Witten/ Donaldson-Thomas theory and birational/symplectic invariants of algebraic surfaces

Project area: Gromov-Witten/ Donaldson-Thomas theory and birational/symplectic invariants of algebraic surfaces

The project aims at proving the connections between DT theory of compactly supported sheaves with two dimensional support, in non-compact local-surface Calabi Yau 3 folds and 4 folds, and rationality of the supporting surface of the sheaf. More precisely, to establish the conjecture: "An algebraic surface with exceptional collection in its derived category is rational". The potential postdoc is expected to have complete familiarity with algebraic geometry, especially Donaldson-Thomas/ Gromov-Witten theories, birational geometry, especially derived categorical approach to birational geometry. If relevant, the position may include a research stay at Harvard University’s Center for Mathematical Sciences and Applications.

Funding agency: IRFD, Independent Research Fund Denmark

Expected duration of the project: 12 to 24 months

Constraint: Applicants for this project must have obtained their PhD degree after 1 August 2017. In case of maternity/paternity leave taken after obtaining the PhD, subtract 2 times the months of leave from the above date.

Host: Assoc. Prof. Artan Sheshmani

(PD-5) Degeneration of virtual moduli cycles for moduli space of coherent sheaves over Calabi-Yau 4 folds

Project area: Degeneration of virtual moduli cycles for moduli space of coherent sheaves over Calabi-Yau 4 folds

The project aims at proving an analog of Graber-Pandharipande degeneration technique for moduli spaces of coherent sheaves over Calabi-Yau 4 folds. The project aims at using both algebraic-geometric and derived algebraic-geometric approaches. In particular one of the main goals of the project is to construct a well-behaved degeneration family for the algebraic virtual fundamental cycles constructed by Thomas and Oh over the moduli spaces of sheaves on compact Calabi Yau fourfolds. The potential postdoc is expected to have complete familiarity with algebraic geometry, especially intersection theory, Donaldson-Thomas/ Gromov-Witten theories, and derived algebraic geometry. If relevant, the position may include a research stay at Harvard University’s Center for Mathematical Sciences and Applications.

Funding agency: IRFD, Independent Research Fund Denmark

Expected duration of the project: 12 to 24 months

Constraint: Applicants for this project must have obtained their PhD degree after 1 August 2017. In case of maternity/paternity leave after obtaining the PhD, subtract 2 times the months of leave from the above date

Host: Assoc. Prof. Artan Sheshmani.