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I am a PhD in Mathematics and AI. I am currently an AI researcher at FOI - Swedish Defence Research Agency.
I did my PhD at KTH Royal Institute of Technology as part of WASP - Wallenberg AI, Autonomous Systems and Software Program. My thesis studies Computer Vision using Algebraic Geometry.
Interests in AI
Generative AI
Reinforcement Learning
Hobbies
Cooking
Long Distance Running
Painting
Music
Horror Movies
Current Position
AI researcher at FOI - Swedish Defence Research Agency
Interests in Applied Algebra
Algebraic Vision
Machine Learning
Algebraic Statistics
Interests in Number Theory
Study of tuples of isospectral non-congruent lattices
PhD
PhD in mathematics at KTH Royal Institute of Technology
Supervisors: Kathlén Kohn, Fredrik Viklund
Funding: Wallenberg AI, Autonomous Systems and Software Program (WASP)
Popular Science Research Overview
Popular Science Research Overview
Aritificial intelligence (AI) is advancing rapidly and, in some areas, can now match or even surpass human cognitive performance. It powers tools that generate realistic images and videos, automate repetitive tasks, and assist researchers with complex analysis. Like all powerful technologies, AI can be used for both beneficial and harmful purposes. For example, large language models can be misused to create fake articles or control automated social media accounts. In defense, reinforcement learning can help optimize combat strategies.
My research explores how AI methods can enhance national defense capabilities, helping to strengthen Sweden and its allies.
Applied algebra uses mathematical structures—such as polynomials, matrices, and groups—to solve real-world problems in statistics, machine learning, computer vision, biology, chemistry, and more. A central tool in this field is algebraic geometry, which studies the solutions of systems of polynomial equations. Algebraic geometry shows up in many applications: in statistics, many important models are defined by polynomial equations; in machine learning, polynomial activation functions make models more interpretable; and in computer vision, even basic cameras can be modeled using algebraic equations.
My research focuses on two directions: the complexity of algebraic optimization and the development of new algorithms for 3D reconstruction. In this context, the goal is to generate a 3D model of a real-world object using multiple 2D images.
Number theory of quadratic forms is a classical area of mathematics that deals with equations involving squares of variables—like x² + y². These are part of a broader category known as Diophantine equations, named after the ancient Greek mathematician Diophantus of Alexandria, who lived in the 3rd century CE. While linear equations are easy to solve, quadratic ones are the first to pose deeper challenges. A natural question is: if two quadratic forms represent the same set of values over the integers, are they necessarily the same? There is beauty to be found in the fact that this question can be reinterpreted through lattice geometry, spectral geometry, and acoustics.
My research studies how many distinct (positive definite) quadratic forms in each dimension can share the same set of values over the integers, a problem only solved in dimensions 1,2, and 3.
AGAVE Reading Group - Active from May 2022 to June 2024
AGAVE Reading Group - Active from May 2022 to June 2024
Myself, Elima Shehu and Angélica Torres organized this reading group in algebraic vision. Website: https://sites.google.com/view/agave-mission/hem.
Preprints
Number Theory
Three's Company in Six Dimensions: Irreducible, Isospectral, Non-Isometric Flat Tori (2024)
with Gustav Mårdby and Julie Rowlett.
Preprint: https://arxiv.org/abs/2412.16709
Algebraic Vision
A Framework for Reducing the Complexity of Geometric Vision Problems and its Application to Two-View Triangulation with Approximation Bounds (2025)
with Georg Bökman, Fredrik Kahl, and Kathlén Kohn
Preprint: https://arxiv.org/pdf/2503.08142
Projections of Curves and Conic Multiview Varieties (2024)
with Isak Sundelius.
Preprint: http://arxiv.org/abs/2404.03063
Metric Multiview Geometry - a Catalogue in Low Dimensions (2024)
with Timothy Duff.
Preprint: https://arxiv.org/abs/2402.00648
Projections of Higher Dimensional Subspaces and Generalized Multiview Varieties (2023)
single-authored.
Preprint: https://arxiv.org/abs/2309.10262
Accepted and Published Articles
Algebraic Vision
Geometric Interpretations of Compatibility for Fundamental Matrices (2025)
with Erin Connelly.
Journal of Symbolic Computation, Volume 131, November–December 2025, 102446
Preprint: https://arxiv.org/abs/2402.00495
Revisiting Sampson Approximation for Geometric Estimation Problems (2024)
with Viktor Larsson and Angélica Torres.
Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 4990-4998
Preprint: https://arxiv.org/abs/2401.07114
Line Multiview Ideals (2024)
with Paul Breiding, Timothy Duff, Lukas Gustafsson and Elima Shehu.
Communications in Algebra, 52(10), 4204–4225
Preprint: http://arxiv.org/abs/2303.02066
Compatibility of Fundamental Matrices for Complete Graphs (2023)
with Martin Bråtelund.
Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. p. 3328-3336
Preprint: https://arxiv.org/abs/2303.10658
Theoretical and Numerical Analysis of 3D Reconstruction Using Point and Line Incidences (2023)
with Elima Shehu and Angélica Torres.
Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. p. 3748-3757
Preprint: https://arxiv.org/abs/2303.13593
Line Multiview Varieties (2023)
with Paul Breiding, Elima Shehu and Angélica Torres.
SIAM Journal on Applied Algebra and Geometry, 2023, 7.2: 470-504
Preprint: https://arxiv.org/abs/2203.01694
Number Theory
The Isospectral Problem for Flat Tori from Three Perspectives (2023)
with Erik Nilsson and Julie Rowlett.
Bulletin of the American Mathematical Society, 2023, 60.1: 39-83
Preprint: https://arxiv.org/abs/2110.09457
Metric Algebraic Geometry
Caustics by Refraction of Circles and Lines (2025)
single-authored.
Acta Univ. Sapientiae Math. 17, 7 (2025)
Preprint: https://arxiv.org/abs/2402.00475
Algebraic Geometry
Adjoints and Canonical Forms of Polypols (2024)
with Kathlén Kohn, Ragni Piene, Kristian Ranestad, Boris Shapiro, Rainer Sinn, Miruna-Stefana Sorea and Simon Telen.
Doc. Math. 30 (2025), no. 2, pp. 275–346
Preprint: http://arxiv.org/abs/2108.11747
Algebraic Statistics
Nets of Conics (2021)
with Stefan Dye, Kathlén Kohn and Rainer Sinn. Part of the LSSM Collaborative Project.
Le Mathematiche, Special Issue on Linear Spaces of Symmetric Matrices, pages 399-414
Preprint: https://arxiv.org/abs/2011.08989
A Selection of Illustrations
The Infinite Euclidean Distance Discriminant
For surfaces in 3-space, skew-tubes are unions of circles such that the normal lines along these circles intersect in a point. The union of all intersection points forms a curve. Each point of this curve has infinitely many ED-critical points on the surface. To the left is a skew-tube around a twisted cubic. This surface is given by a degree-10 polynomial of 123 terms.
Projection of Curves and Conic Multiview Varieties
Two back-projected cubic cones are shown, through the two green centers. The twisted cubic defining the cones is illustrated in thick orange. The surfaces also intersect in a degree-6 curve drawn in thin orange. Indeed, since the surfaces are degree-3, the expected total degree of the intersection is 9.
Caustics by Refraction of Circles and Lines
Refracted rays (in blue and orange) given a black radiant point and a black ellipse. As Bruce and Giblin (1992) write, "These [lines] appear to cluster along another curve, which the eye immediately picks out ... The new curve is called the envelope."
Revisiting Sampson Approximation for Geometric Estimation Problems
This figure illustrates the Sampson approximation scheme for the purpose of fitting data to an algebraic variety. Here, our mathematical model is the ellipse C(x, y) = x^2+2y^2−4 = 0.
Theoretical and Numerical Analysis of 3D Reconstruction Using Point and Line Incidences
We studied how to best reconstruct point and line such that incidence relations are preserved. The left picture illustrates individual triangulation of the points and line, and the right picture illustrates a reconstruction algorithm which ensures that the reconstructed points lie on the reconstructed line.
Line Multiview Varieties
The main theorem of line multiview varieties is says that a line multiview variety is cut out by the condition that the back-projected planes meet in a line if and only if the centers are pairwise disjoint and no four centers are collinear. The foundational idea for its proof uses basic theory of smooth quadrics and is illustrated in the image to the right.
Graduate Student Meeting on Applied Algebra and Combinatorics, KTH April 2023
Graduate Student Meeting on Applied Algebra and Combinatorics, KTH April 2023
Myself, Xiangying Chen, Danai Deligeorgaki, Oskar Henriksson, Filip Jonsson Kling and Mariel Supina organized a conference for young researches on applied algebra and combinatorics, with plenary speakers Carlos Améndola and Kris Shaw.
WASP AI Courses
Autonomous Systems, 2022
Artificial Intelligence and Machine learning, 2022
Ethical, Legal and Societal Aspects on AI and Autonomous Systems, 2022
Topological Data Analysis, 2021
AI Deep Learning and GANs, 2021
Modern Topics in Artificial Intelligence, 2020
WASP Activities
WASP Winter Conference 2025
WASP Winter Conference 2024
WASP Summer School on Public Safety 2023
WASP Digital Career Day 2023
WASP Winter Conference 2023
WASP Summer School on Synthesis of Human Communication 2022
WASP Winter Conference 2021
Talks and Posters
2024
Revisiting Sampson Approximation for Geometric Estimation Problems, CVPR
Nearest Point Problems in Computer Vision, SISSA
2023
Euclidean Distance Degrees Associated to Families of Rational Maps, University of Wisconsin
Compatibility of Fundamental Matrices for Complete Graphs, SIAM
Nets of Conics, Univsersitat Autónoma de Barcelona
Lines in Algebraic Vision, RSME
Algebraic Vision Poster, WASP Winter Conference
2022
Triangulation in Algebraic Vision, CATS seminar KTH
A Generalized Multiview Variety, VŠCHT
The Multiview Variety, MPI Leipzig
Mathematical Modelling of Cameras, PhD Fest Stockholm
2021
Nets of Conics Poster, MEGA Conference
Nets of Conics, LSSM Seminar
Research Activities
Attended Conferences
NeurIPS Conference on Neural Information Processing Systems, Vancouver, Canada (2024)
MEGA: Effective Methods in Algebraic Geometry, Leipzig, Germany (2024)
CVPR Conference on Computer Vision and Pattern Recognition, Seattle, USA (2024)
ICCV International Conference on Computer Vision, Paris, France (2023)
SIAM Conference on Applied Algebraic Geometry, Eindhoven, The Netherlands (2023)
Graduate Student Meeting on Applied Algebra and Combinatorics (2023)
RSME León, Spain (2023)
Geometry in Complexity and Computation, Konstanz, Germany (2022)
CCAAGS, Seattle, USA (2022)
Mathematics for Complex data, Stockholm, Sweden (2022)
MEGA: Effective Methods in Algebraic Geometry, online (2021)
SIAM Annual Meeting, online (2021)
Visits
University of Wisconsin (2023)
University of Washington (2023)
Univsersitat Autónoma de Barcelona (2023)
VŠCHT: University of Chemistry and Technology, Prague (2022)
MPI, Leipzig (2022)
Workshops
Metric Algebraic Geometry, Oberwolfach, Germany (2023)
REACT: Research Encounters in Algebraic and Combinatorial Topics, online (2021)
Graduate Student Meeting on Applied Algebra and Combinatorics, online (2021)
Teaching
Teaching Experience
I have been teaching assistant for 14 undergraduate math courses at the University of Gothenburg and KTH
FLH3000: Basic communication and teaching
Teaching Assistance at KTH
Discrete Mathematics SF1662, 2020
Discrete Mathematics SF1671, 2020-2022
Advanced Linear Algebra SF1681, 2021-2022
Supervision
Bachelor's thesis at Chalmers in number theory, spring of 2024. Students: Madicken Astorsdotter, Filippa Hultin and William Karlsson.
Education
Bachelor's Degree, 2016-2019: Pure mathematics at the University of Gothenburg.
Master's Degree, 2019-2020: Pure mathematics at the University of Gothenburg
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