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Timothy Duff

NSF Mathematical Sciences Postdoctoral Fellow & Postdoctoral Scholar
Department of Mathematics, University of Washington
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Email:      Office: Padelford Hall C-505

I am a postdoc in the math department of University of Washington, mentored by Rekha Thomas. I received a PhD in Algorithms, Combinatorics, and Optimization, advised by Anton Leykin at Georgia Tech. My reserach interests include computational and combinatorial aspects of algebraic geometry, algorithms for polynomial system solving and their implementation, and applications of these techniques to problems like 3D reconstruction in computer vision.

In Fall 2024 I will be an assistant professor of mathematics at the University of Missouri in Columbia.

Preprints / Under Review

  1. Algebra and Geometry of Camera Resectioning (With Erin Connelly, Jessie Loucks-Tavitas.)
  2. Geometric Solution to the Angles-Only Initial Orbit Determination Problem.
    (With Michela Mancini, John Christian, Anton Leykin.)
    Conference version: 2022 AAS/AIAA Astrodynamics Specialist Conference.
  3. Line Multiview Ideals. (With Paul Breiding, Lukas Gustafsson, Felix Rydell, Elima Shehu.)
  4. SubalgebraBases in Macaulay2. (With Michael Burr, Oliver Clarke, Jackson Leaman, Nathan Nichols, Elise Walker.)

Research Publications

    Where applicable, conference and journal versions are listed together.
    Please be advised that final versions may only be available through publishers.

  1. Using monodromy to recover symmetries of polynomial systems
    (With Viktor Korotynskiy, Tomas Pajdla, Margaret Regan.)
    Extended version under review
    Conference version in proceedings of ISSAC 2023.
  2. Four-view geometry with unknown radial distortion
    (With Petr Hruby, Viktor Korotynskiy, Luke Oeding, Marc Pollefeys, Tomas Pajdla, Viktor Larsson.) Proceedings of CVPR 2023.
  3. u-generation: solving systems of polynomials equation-by-equation
    (With Jose Israel Rodriguez , Anton Leykin.) Numerical Algorithms, 2023.
  4. Learning to Solve Hard Minimal Problems (With Petr Hrubý, Anton Leykin, Tomas Pajdla.)
    To appear in a special issue of TPAMI, 2023.
    Conference version: Proceedings of CVPR 2022. Won best paper!
  5. Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
    (With Viktor Korotynskiy, Tomas Pajdla, Margaret Regan.)
    SIAM Journal on Applied Algebra and Geometry, 2023.
  6. Trifocal Relative Pose From Lines at Points
    (With Ricardo Fabbri , Hongyi Fan , Margaret Regan, David da Costa de Pinho, Elias Tsigaridas, Charles Wampler, Jonathan Hauenstein, Benjamin Kimia, Anton Leykin, Tomas Pajdla.) TPAMI, 2023. Conference version: Proceedings of CVPR 2020.
  7. Signatures of algebraic curves via numerical algebraic geometry (With Michael Ruddy.)
    Journal of Symbolic Computation, 2023. Conference version: Proceedings of ISSAC 2020.
  8. Polyhedral homotopies in Cox coordinates (With Simon Telen, Elise Walker, Thomas Yahl.)
    Journal of Algebra and Its Applications, 2023.
  9. An Atlas for the Pinhole Camera (With Sameer Agarwal, Max Lieblich, Rekha Thomas.)
    Foundations of Computational Mathematics, 2022.
  10. Certification for polynomial systems via square subsystems
    (With Nickolas Hein and Frank Sottile.) Journal of Symbolic Computation, 2022.
    Extended abstact presented at MEGA 2019.
  11. PL1P---Point-line minimal problems under partial visibility in three views
    (With Kathlén Kohn, Anton Leykin, Tomas Pajdla.)
    Accepted to IJCV. Conference Version: ECCV 2020.
  12. PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility
    (With Kathlén Kohn, Anton Leykin, Tomas Pajdla.) To appear in TPAMI, 2023.
    Conference version: Proceedings of ICCV 2019, Won best student paper!
  13. Monodromy solver: sequential and parallel (With Nathan Bliss, Anton Leykin, Jeff Sommars.)
    Proceedings of ISSAC 2018.
  14. Solving polynomial systems via homotopy continuation and monodromy (With Cvetelina Hill, Anders Jensen, Kisun Lee, Anton Leykin, Jeff Sommars.)
    IMA Journal of Numerical Analysis, 2018.
  15. Polynomial automata: Zeroness and applications (With Micheal Benedikt, Aditya Sharad, James Worrell.) Proceedings of LICS 2017.
  16. Robust graph ideals (With Adam Boocher, Bryan Brown, Laura Lyman, Takumi Murayama, Amy Nesky, Karl Schaefer.) Annals of Combinatorics, 2015.

Expository Publications

  1. Polynomial systems, homotopy continuation, and applications. (With Margaret Regan.)
    Notices of the American Mathematical Society, 2022
  2. Nonlinear Algebra and Applications (With Paul Breiding, Türkü Özlüm Çelik, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, Oğuzhan Yürük.)
    Numerical Algebra, Control, and Optimization, 2021.


At University of Washington