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Staff photo Per Åhag

Per Åhag

Docent in Mathematics. Focus: artificial intelligence in the VR-funded project “Neural Differential Equations on M-polyfolds” and applied research in the project “Energy Transition in Everyday Life” financed by the Swedish Energy Agency.

Research qualifications: Docent

Works as

Affiliation
Location
MIT-huset, plan 3, Matematik och matematisk statistik, MIT.F.349 Umeå universitet, 901 87 Umeå

Since embarking on my mathematical journey over thirty years ago, my passion for this inspiring discipline has not waned, but has instead continued to flourish. From the moment I began exploring its intricate layers, I was captivated by the beauty and power of mathematics, a foundational pillar that upholds modern society.

My professional journey has not merely been about unveiling the mysteries of mathematics through research and teaching, but also about helping to shape and nurture a vibrant and sustainable mathematical community for the future.

My research primarily spans the fascinating realms of several complex variables, pluripotential theory, and differential geometry. This includes deep explorations of topics ranging from Kähler geometry to polyfold theory. Yet, like all restless and curious researchers, I venture beyond these domains. Such excursions include the Lenz–Ising model in statistical mechanics, in-depth work on elasticity problems, Schmeidler’s expected utility model in finance, and MIMO (Multi-Input Multi-Output) in wireless communication. At present, this curiosity has guided me toward a strong focus on geometric deep learning, including work within the project “Neural Differential Equations on M-polyfolds” and in stochastic geometry, as well as toward questions in urban and regional planning.

Recognizing the inherent beauty of mathematics, I believe in making it accessible and meaningful to a broader audience. This conviction has led me to explore educational psychology and to study the perceptions held by specific student groups. This interest both satisfies my own curiosity and contributes to refining and enriching my teaching.

Beyond the world of definitions and theorems, I spend much of my time on the sidelines, cheering on my son during his training sessions and sporting events. And when the universe grants me its rare moments of rest, I can often be found in the heart of my kitchen, where I experiment with flavors, cooking up a storm, or bake imaginative creations.

Konferensbidrag 10:e Utvecklingskonferensen f枚r Sveriges ingenj枚rsutbildningar, Karlskrona: Blekinge Tekniska H枚gskola 2025 : 167-175
Bjurulf, Harald; Westin, Jonas; 脜hag, Per
Tilde: rapporter fr氓n Institutionen f枚r estetiska 盲mnen
Bjurulf, Harald; Westin, Jonas; 脜hag, Per
Acta Mathematica Vietnamica, Springer 2025, Vol. 50, (2) : 285-301
Granath, Andreas; 脜hag, Per; Per盲l盲, Antti; et al.
International Journal of Mathematical Education in Science and Technology, Taylor & Francis 2025, Vol. 56, (11) : 2236-2250
Hed, Lisa; 脜hag, Per; Norqvist, Mathias
Annales Polonici Mathematici, Institute of Mathematics, Polish Academy of Sciences 2025, Vol. 134, (1) : 1-18
脜hag, Per; Czy偶, R.; Lundow, Per-H氓kan
Annales Academiae Scientiarum Fennicae Mathematica Dissertationes, Finnish Mathematical Society 2025, Vol. 50, (1) : 201-214
脜hag, Per; Czy偶, Rafa艂
Proceedings of the American Mathematical Society, American Mathematical Society (AMS) 2025, Vol. 153, (8) : 3381-3394
脜hag, Per; Czy偶, Rafa艂
Mathematische Annalen, Springer Nature 2025, Vol. 91 : 3333-3361
脜hag, Per; Czy偶, Rafa艂; Lu, Chinh H.; et al.
2024 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM) : 0001-0005
Westin, Jonas; Olsson, Leif; 脜hag, Per
2024 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE 2024 : 400-404
Westin, Jonas; Olsson, Leif; 脜hag, Per
Applied Mathematics and Computation, Elsevier 2024, Vol. 462
脜hag, Per; Czy偶, R.; Lundow, Per-H氓kan
Mathematische Zeitschrift, Springer Nature 2024, Vol. 308, (4)
脜hag, Per; Czy偶, Rafa艂; Lu, Chinh H.; et al.
Bidrag fr氓n den 9:e utvecklingskonferensen f枚r Sveriges ingenj枚rsutbildningar, V盲ster氓s: M盲lardalens universitet 2023 : 318-323
Hed, Lisa; Granath, Andreas; 脜hag, Per
N盲mnaren : tidskrift f枚r matematikundervisning, G枚teborgs universitet 2023, (4) : 81-84
Hed, Lisa; Leijon, Rasmus; 脜hag, Per
International mathematics research notices, Oxford University Press 2023, Vol. 2023, (12) : 10115-10155
脜hag, Per; Czy偶, Rafa艂
Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, Scuola Normale Superiore 2023, Vol. 24, (3) : 1853-1873
脜hag, Per; Czy偶, Rafa艂
2023 IEEE International Conference on Industrial Engineering and Engineering Management, IEEE 2023 : 903-907
脜hag, Per; Hed, Lisa; Leijon, R.; et al.
New York Journal of Mathematics, Electronic Journals Project 2022, Vol. 28 : 958-969
Eskandari, Setareh; Abkar, Ali; 脜hag, Per; et al.
Journal of Geometric Analysis, Springer 2022, Vol. 32, (4)
脜hag, Per; Czy偶, Rafa艂
Proceedings of the American Mathematical Society, American Mathematical Society (AMS) 2022, Vol. 150, (12) : 5311-5320
脜hag, Per; Czy偶, Rafa艂
N盲mnaren : tidskrift f枚r matematikundervisning, G枚teborgs universitet 2020, Vol. 46, (4) : 25-31
Hed, Lisa; Sande, Olow; 脜hag, Per
Results in Mathematics, Springer 2020, Vol. 75, (2)
脜hag, Per; Czyz, Rafal
Mathematica Scandinavica, Copenhagen: Societates Mathematicae 2020, Vol. 126, (3) : 497-512
脜hag, Per; Czyz, Rafal; Hed, Lisa
Complex Variables and Elliptic Equations, Taylor & Francis 2020, Vol. 65, (2) : 152-177
脜hag, Per; Czy偶, Rafa艂; Hed, Lisa
2020 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE 2020 : 1266-1270
脜hag, Per; Hsu, Y.J.; Olsson, L.; et al.
Annales Polonici Mathematici, Polish Academy of Sciences 2019, Vol. 123, (1) : 15-20
脜hag, Per; Cegrell, Urban; Hiep, Pham Hoang
Annales Polonici Mathematici, Polish Academy of Sciences 2019, Vol. 123, (1) : 21-29
脜hag, Per; Czyz, Rafal
Journal of Mathematical Analysis and Applications, Elsevier 2019, Vol. 479, (2) : 1456-1474
脜hag, Per; Czy偶, Rafa艂
2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE 2019 : 224-227
脜hag, Per; Hed, Lisa; Lundow, Per-H氓kan; et al.
Journal of Geometric Analysis, Springer 2018, Vol. 28, (4) : 3196-3222
脜hag, Per; Czyz, Rafal; Hed, Lisa
Experimental Mathematics, Philadelphia: Taylor & Francis 2018, Vol. 27, (1) : 119-124
脜hag, Per; Czyz, Rafal; Lundow, Per-H氓kan
Complex Variables and Elliptic Equations, Taylor & Francis 2018, Vol. 63, (6) : 783-801
脜hag, Per; Czy偶, Rafa艂; Hed, Lisa
Universitatis Iagellonicae Acta Mathematica, Jagiellonian University 2017, Vol. 54 : 7-13
脜hag, Per; Czyz, Rafa艂
Journal of Mathematical Analysis and Applications, Vol. 422, (2) : 960-980
脜hag, Per; Cegrell, Urban; Czyz, Rafal
Journal of Mathematical Analysis and Applications, Vol. 423 : 94-105
脜hag, Per; Cegrell, Urban; Ph岷, Ho脿ng Hi峄噋
Complex Variables and Elliptic Equations, Vol. 60, (9) : 1270-1276
脜hag, Per; Czyz, Rafal
Archiv der Mathematik, Springer 2015, Vol. 105, (4) : 371-380
脜hag, Per; Czy偶, Rafa艂
Mathematica Scandinavica, Aarhus, Denmark: University of Munkegade 2012, Vol. 110, (2) : 235-250
脜hag, Per; Cegrell, Urban; Czyz, Rafal
Universitatis Iagellonicae Acta Mathematica, Krakow: Instytut Matematyki Uniwersytetu Jagiellonskiego 2012, Vol. 50 : 7-23
脜hag, Per; Czyz, Rafal
Annales Polonici Mathematici, Vol. 106 : 1-17
脜hag, Per; Czyz, Rafal; Persson, Leif
Osaka Journal of Mathematics, Vol. 47, (3) : 637-650
脜hag, Per; Cegrell, Urban; Pham, Hoang Hiep
Journal of Mathematical Analysis and Applications, Vol. 361, (2) : 302-321
脜hag, Per; Czyz, Rafal
Journal des Math茅matiques Pures et Appliqu茅es, Vol. 92, (6) : 613-627
脜hag, Per; Cegrell, Urban; Czyz, Rafal; et al.
Advances in Mathematics, Vol. 222, (6) : 2036-2058
脜hag, Per; Cegrell, Urban; Kolodziej, Slawomir; et al.
Journal of inequalities and applications : 901397-8 pages
脜hag, Per; Czyz, Rafal
IEEE Conference on Local Computer Networks (LCN'08), 14-17 Oct. 2008, Montreal, Canada
Gidlund, Mikael; 脜hag, Per
Doctoral thesis / Ume氓 University, Department of Mathematics, 25
脜hag, Per