Research
Most of my research is related to differential and/or algebraic geometry. I'm interested in canonical metrics on complex manifolds and their relations to algebro-geometric stability and concepts in probability theory. Along another line, I'm also interested in canonical metrics on certain real (affine) manifolds related to the Strominger-Yau-Zaslov conjecture in mirror symmetry. The main tools I use in my research come from geometric analysis.
Foto: Per Åhag
Publications and Preprints
Duality of Hessian manifolds and optimal transport
https://arxiv.org/abs/2306.11819
To appear in Convex and Complex: Perspectives on Positivity in Geometry, AMS Contemporary Mathematics (CONM)
Solvability of Monge-Ampère equations and tropical affine structures on reflexive polytopes
(with Rolf Andreasson)
https://arxiv.org/abs/2303.05276
Tropical and non-Archimedean Monge--Ampère equations for a class of Calabi--Yau hypersurfaces
(with Mattias Jonsson, Enrica Mazzon, Nicholas McCleerey)
To appear in Advances in Mathematics
Optimal Transport for Super Resolution Applied to Astronomy Imaging. (Michael Rawson, Jakob Hultgren)
European Signal Processing Conference (EUSIPCO) 2022
Mutual asymptotic Fekete sequences
Extremal potentials and equidistribution measures associated to collections of Kähler classes
Mathematische Zeitschrift
DOI: https://doi.org/10.1007/s00209-021-02964-8 (link to full text: https://rdcu.be/cFpdw)
Unipotent Factorization of Vector Bundle Automorphisms (with Erlend F. Wold)
International Journal of Mathematics Vol. 32, No. 03, 2150013 (2021)
DOI: https://doi.org/10.1142/S0129167X21500130 (also at arXiv:1911.13240)
Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds (with Thibaut Delcroix)
Journal de Mathématiques Pures et Appliquées Volume 153, September 2021, Pages 281-315
DOI: https://doi.org/10.1016/j.matpur.2020.12.002 (also at arXiv:1812.07218)
Coupled Kähler-Ricci Solitons on Toric Fano Manifolds
Analysis & PDE Volume 12 (2019), No. 8, Pages 2067–2094
DOI: 10.2140/apde.2019.12.2067 (older version available at arXiv:1607.02923)
Coupled Kähler-Einstein Metrics (with David Witt Nyström)
International Mathematics Research Notices Volume 2019, Issue 21, November 2019, Pages 6765–6796
DOI: https://doi.org/10.1093/imrn/rnx298 (older version available at arXiv:1608.07209)
An Optimal Transport Approach to Monge-Ampère Equations on Compact Hessian Manifolds (with Magnus Önnheim)
Journal of Geometric Analysis Volume 29, Issue 3, July 2019, Pages 1953–1990
DOI: https://doi.org/10.1007/s12220-018-0068-5 (open access)
Permanental Point Processes on Real Tori, Theta Functions and Monge-Ampère Equations
Annales de la faculté des sciences de Toulouse: Mathématiques, Serie 6, Volume 28 (2019) no. 1, Pages 11-65
DOI : https://doi.org/10.5802/afst.1592 (open access)
Other
Some plots of the Monge-Ampère metric on the boundary of the unit simplex, related to the SYZ-conjecture and joint work with Andreasson, Jonsson, Mazzon and McCleerey.
The first chapter of my thesis (approx 30 pages) contains a brief introduction to Kähler Geometry, affine manifolds, canonical metrics and the probabilistic parts (N-particle point processes and large deviation principles) used in my first four papers
Lecture notes from a colloquium about canonical metrics in complex geometry I held at the University of Oslo in February, 2019
My master's thesis, containing an exposition of Fedor Nazarov's complex analytic proof of the Bourgain-Milman theorem.