Felix Rydell

I'm a fourth year PhD student at KTH, Stockholm. My research investigates and builds connections between artificial intelligence and applied algebraic geometry.

Research Interests

Applied algebra motivated by Artificial Intelligence

Hobbies

Current Position

PhD in mathematics at KTH Royal Institute of Technology

AGAVE Reading Group

Myself and Elima Shehu are organizing a reading group in algebraic vision.

Website: https://sites.google.com/view/agave-mission/hem

Preprints

Algebraic Vision

with Sundelius.

Preprint: http://arxiv.org/abs/2404.03063

with Duff.

Preprint: https://arxiv.org/abs/2402.00648

with Connelly.

Preprint: https://arxiv.org/abs/2402.00495 

with Myself.

Preprint: https://arxiv.org/abs/2309.10262                                         

Metric Algebraic Geometry

with Myself.

Preprint: https://arxiv.org/abs/2402.00475         

Algebraic Geometry 

with Kohn, Piene, Ranestad, Shapiro, Sinn,  Sorea and Telen.

Preprint: http://arxiv.org/abs/2108.11747                                                                       

Accepted and Published Articles

Algebraic Vision

with Larsson and Torres. Accepted for publication in CVPR 2024.

Preprint: https://arxiv.org/abs/2401.07114  

with Breiding, Duff, Gustafsson and Shehu. Accepted for publication in Communications in Algebra.

Preprint: http://arxiv.org/abs/2303.02066    

with Bråtelund. Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. p. 3328-3336. 

Preprint: https://arxiv.org/abs/2303.10658

with Shehu and Torres.  Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023. p. 3748-3757.

Preprint: https://arxiv.org/abs/2303.13593     

with Breiding, Shehu and Torres. SIAM Journal on Applied Algebra and Geometry, 2023, 7.2: 470-504. 

Preprint: https://arxiv.org/abs/2203.01694

Algebraic Statistics

with Dye,  Kohn and 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 

Number Theory

with Nilsson and Rowlett.  Bulletin of the American Mathematical Society, 2023, 60.1: 39-83.

Preprint: https://arxiv.org/abs/2110.09457                                                             

A Selection of Illustrations

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.

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.

Refracted rays (in blue and orange,) given the black radiant point A and the black circle C. The red curve is the complete caustic by refraction, and the green curves are the Caustic ovals, whose evolute is the red curve. The blue lines are correspond to the refraction constant n = 1/2 and the orange lines correspond to n = −1/2. 

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. 

For this project, we studied how to best reconstruct point and line such that incidence relations are preserved.  Method (L1).0 refers to individual triangulation of the points and line, and method (L1).1 is a reconstruction algorithm ensuring that the reconstructed points lie on the reconstructed line. 

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

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.  

Website: https://sites.google.com/view/applied-alg-comb-2023/graduate-student-meeting-on-applied-algebra-and-combinatorics

WASP AI Courses


WASP Activities

Talks and Posters

2023

2022

2021

Research Activities

Attended Conferences

Visits

Workshops

Teaching 

Teaching Experience

Teaching Assistance at KTH

Supervision

Education

Contact Information

felixry@kth.se