Project description

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.

Short bio

Dyrefelt's research is in pure mathematics, in the areas of Complex Differential- and Algebraic Geometry. After earning his PhD from École Polytechnique in Paris and Université Paul Sabatier in Toulouse, he has held postdoctoral research positions at CTH in Göteborg, Sweden, and the International Centre for Theoretical Physics (ICTP). Before joining AIAS he will hold the SISSA Mathematical Fellowship in Trieste, Italy.