Mathematicians often deal with very high dimensional spaces, which are studied abstractly for their own sake, but also arise naturally in a wide variety of scientific disciplines. Examples include “state spaces” in physics, “big data”, and the string theoretic description of our universe, which according to one theory is 10-dimensional, with 4 dimensions accounted for by space time and 6 dimensions compactified into a so-called Calabi-Yau threefold. The guiding question of my field of research is to understand geometric properties about such spaces, allowing us to “see them” through our equations.
The proposed AIAS-COFUND II project is purely theoretical and will study several open questions in complex geometry, all related to a mathematical prediction made in the 1990’s, named the Yau-Tian-Donaldson conjecture after its inventors. The main cross-disciplinary aspect of the project is to improve theoretical understanding of *entropy*, which has historically been a central concept in many scientific theories, but whose appearance in the Kähler geometry branch of modern mathematics has unveiled a number of challenging questions that remain to be answered.
Project title: Stable and unstable mathematical shapes
Area of research: Mathematics
Fellowship period: 1 Feb 2022 - 31 Jan 2025
Fellowship type: AIAS-COFUND II Marie Skłodowska-Curie fellow
This fellowship has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754513 and The Aarhus University Research Foundation.