Applied & Computational Algebraic Geometry

Elima Shehu

Postdoctoral Researcher · MathCoRe Research Training Group, Otto von Guericke University Magdeburg

I study systems of polynomial equations that arise in computer vision — the algebra and geometry behind reconstructing the 3D world from images.

Portrait of Elima Shehu
01

About

I work at the meeting point of algebra, geometry, and computation — using polynomial systems to answer concrete questions in computer vision and statistics.

I am a postdoctoral researcher in the MathCoRe Research Training Group at Otto von Guericke University Magdeburg. I completed my Ph.D. in Mathematics at Osnabrück University in April 2024, under the supervision of Paul Breiding.

From 2021 to 2024 I was a doctoral researcher in the Emmy Noether Group, hosted by the Max Planck Institute for Mathematics in the Sciences in Leipzig. My research lies in applied and computational algebraic geometry, focusing on the polynomial equations behind algebraic vision and algebraic statistics.

Outside mathematics, I enjoy time in nature, cooking cuisines from around the world, and discovering new places through travel.

Position
Postdoctoral Researcher · MathCoRe RTG, OVGU Magdeburg
PhD in Mathematics
Osnabrück University · April 2024, adv. Paul Breiding
Fields
Algebraic Vision · Computer Vision · Algebraic Statistics
Based in
Magdeburg, Germany · previously Leipzig & Tirana
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Research

Many geometric problems — reconstructing a scene from photographs, or inferring an evolutionary tree — become systems of polynomial equations. I study the varieties those systems define: their degree, structure, and the algorithms that solve them.

Algebraic Vision

The geometry of 3D reconstruction from images: multiview varieties, point- and line-incidence constraints, and the essential variety underlying two-view geometry.

Multiview varietiesEssential varietyTriangulation

Computational Algebraic Geometry

Turning geometry into computation: numerical algebraic geometry, Gröbner and SAGBI bases, and algorithms for the degree and structure of varieties.

Gröbner / SAGBINumerical AGMacaulay2

Algebraic Statistics

Algebra meets inference: the algebraic degree of phylogenetic varieties and the geometry of statistical models arising in evolutionary biology.

PhylogeneticsAlgebraic degreeModel geometry
03

Publications

Google Scholar

Preprints

1
2026
Preprint E. Shehu, P. Hrubý

Published & Peer-Reviewed

6
2026
ISSAC '26 Honorable Mention V. Borovik, T. Duff, E. Shehu
2024
La Matematica P. Breiding, S. Fairchild, P. Santarsiero, E. Shehu
2024
Algebraic Statistics L. D. García Puente, M. Garrote-López, E. Shehu
2024
Communications in Algebra P. Breiding, T. Duff, L. Gustafsson, F. Rydell, E. Shehu
2023
SIAM J. Appl. Algebra Geom. P. Breiding, F. Rydell, A. Torres, E. Shehu
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Software

SagbiGbDetection.jl

A Julia package for Gröbner & SAGBI basis detection

Given the generators of an ideal — or of a finitely generated subalgebra of a polynomial ring — the package searches for a term order under which those generators form a Gröbner basis, respectively a SAGBI basis. Built on the Oscar.jl computer-algebra system.

Julia Oscar.jl MIT License Borovik · Duff · Shehu

Companion software to the ISSAC '26 paper “SAGBI and Gröbner Bases Detection.”

Julia REPL
julia> using Pkg
julia> Pkg.add(url="https://github.com/elimashehu/SagbiGbDetection.jl")
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Talks & Activities

Invited Talks

  • Geometry and Optimization for 3D Reconstruction
  • Average Degree of the Essential Variety
    Non-linear Algebra Seminar, MPI MiS Leipzig · Dec 2022
  • Line Multiview Varieties
    Algebraic Vision Meeting, Czech Technical University, Prague · May 2022
  • Line Multiview Varieties
    Oberseminar Algebra, Osnabrück University · Apr 2022
  • Line Multiview Varieties
    Non-linear Algebra Seminar, MPI MiS Leipzig · Mar 2022

Conference Talks & Posters

  • SAGBI and Gröbner Bases DetectionTalk
  • 3D Reconstruction Using Point and Line IncidencesPoster
    ICCV, Paris · Oct 2023  ·  Applied Algebra, Osnabrück · Sep 2023
  • Average Degree of the Essential VarietyTalk
    SIAM AG23, Eindhoven · Jul 2023  ·  RMSE Meeting, León · Feb 2023
  • Line Multiview VarietiesTalk
    DMV Workshop, Berlin · Sep 2022  ·  19th EWM General Meeting, Espoo · Aug 2022
  • Line Multiview VarietiesPoster
    CIMPA Summer School, Tirana · Jul 2022
  • Algebraic Degrees of Phylogenetic VarietiesTalk
    MEGA Conference, Kraków · Jun 2022

Organisation

  • Algebraic Vision Minisymposium
    SIAM AG, Eindhoven · Jul 2023
  • Special Day Seminar on Algebraic Geometry
    MPI MiS Leipzig · May 2022
  • Reading group · concluded 2024

Visits & Participation

  • Scientific Visit — KTH Royal Institute of Technology
    Stockholm · Sep 2022
  • Saxonian Seminar Day on Algebra & Geometry
    Dresden · May 2022
  • Convex and Discrete Geometry Day
    Berlin · Mar 2022
  • SIAM AG · MEGA · CVPR
    Virtual · 2021
06

Curriculum Vitae

Education & Positions

  • Postdoctoral Researcher
    Otto von Guericke University Magdeburg — MathCoRe (Mathematical Complexity Reduction)
    Since April 2024
  • Ph.D. in Mathematics
    Osnabrück University & MPI for Mathematics in the Sciences, Leipzig
    April 2024
    Emmy Noether Group — Applied Algebra & Data Analysis · adv. Paul Breiding
  • M.Sc. in Applied Mathematics
    Polytechnic University of Tirana, Albania
    July 2019
    Evaluation: Excellent
  • B.Sc. in Applied Mathematics
    Polytechnic University of Tirana, Albania
    July 2017

Award

ISSAC '26 Honorable Mention
for “SAGBI and Gröbner Bases Detection”, Int. Symposium on Symbolic & Algebraic Computation.

Teaching

  • Assistant Lecturer · Polytechnic University of TiranaCalculus I · Probability Theory · Linear Algebra — 2019–2021
  • Assistant Lecturer · University of Tirana, Faculty of EconomicsMathematics I — 2020–2021

Grants & Visits

  • ICCV Travel Grant — 850 €Paris · October 2023
  • Scientific Visit — KTH StockholmSeptember 2022

Workshops

Let's talk mathematics.

I'm always glad to discuss algebraic vision, computational algebraic geometry, collaborations, or talks. Reach out anytime.