Lukas Liehr

I am a postdoctoral researcher at Bar-Ilan University, working under the supervision of Nir Lev. I completed my Ph.D. in Mathematics at the University of Vienna in 2024, where I was part of the Applied Harmonic Analysis Cluster. Before that, I studied at the Technical University of Munich and Seoul National University.

My research interest centers around harmonic analysis, functional analysis, and formalization of mathematics in Lean.

Google ScholararXivGitHublukas.liehr@biu.ac.il
Lukas Liehr

Publications

2026

  1. Structured coordinate systems in Lp(ℝ)

    D. Freeman, L. Liehr, M. A. TaylorLean formalizationarXivPDF

  2. Phase retrieval from a uniformly discrete point set

    J. de Dios Pont, J. Greilhuber, L. Liehr, M. A. TaylorLean formalizationarXivPDF

  3. Counterexamples to Grad's conjecture

    J. Gómez-Serrano, L. Liehr, M. A. TaylorLean formalizationarXivPDF

  4. Energy minimization for eight points on the sphere

    L. Kryvonos, L. Liehr, M. A. TaylorNumerical certificates & LeanarXivPDF

  5. Universal completeness of exponentials

    S. Bertolini, E. Florit-Simon, L. Liehr, M. A. TaylorLean formalizationarXivPDF

  6. Grothendieck's theorem for Bessel sequences

    L. Liehr, M. A. Taylor, P. YuLean formalizationarXivPDF

  7. Gabor frames of totally positive functions: a complete characterization

    J. de Dios Pont, K. Gröchenig, L. Liehr, I. Shafkulovska, M. A. TaylorLean formalizationarXivPDF

  8. Cantor measures with odd base do not admit Fourier frames

    J. de Dios Pont, L. Liehr, M. A. TaylorLean formalizationarXivPDF

  9. On the existence problem of regular Gabor frames

    J. de Dios Pont, L. Liehr, M. A. TaylorLean formalizationarXivPDF

  10. Compactly supported Gabor orthonormal bases

    L. LiehrarXivPDF

  11. Nonlinear determination and phase retrieval under unimodular constraints

    L. Liehr, T. SzczepanskiarXivPDF

  12. Cheeger's isoperimetric problem for Gaussian mixtures

    L. Liehr·Israel J. Math., acceptedarXivPDF
2025

  1. Phase retrieval in Fock space and perturbation of Liouville sets

    P. Grohs, L. Liehr, M. Rathmair·Rev. Mat. Iberoam. 41, no. 3Journal

  2. Translation-based completeness on compact intervals

    L. Liehr·J. Approx. Theory 305Journal

  3. Multi-window STFT phase retrieval: lattice uniqueness

    P. Grohs, L. Liehr, M. Rathmair·J. Funct. Anal. 288, no. 3Journal

  4. Phaseless sampling on square-root lattices

    P. Grohs, L. Liehr·Found. Comput. Math. 25Journal

  5. From completeness of discrete translates to phaseless sampling of the short-time Fourier transform

    P. Grohs, L. Liehr, I. Shafkulovska·Adv. Comput. Math. 51, no. 28Journal
2024

  1. Arithmetic progressions and holomorphic phase retrieval

    L. Liehr·Bull. Lond. Math. Soc. 56, no. 11Journal

  2. Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality

    P. Grohs, L. Liehr·Constr. Approx. 59, 1Journal
2023

  1. Non-uniqueness theory in sampled STFT phase retrieval

    P. Grohs, L. Liehr·SIAM J. Math. Anal. 55, no. 5Journal

  2. Injectivity of Gabor phase retrieval from lattice measurements

    P. Grohs, L. Liehr·Appl. Comput. Harmon. Anal. 62Journal
2022

  1. On foundational discretization barriers in STFT phase retrieval

    P. Grohs, L. Liehr·J. Fourier Anal. Appl. 28, no. 39Journal
2020

  1. Phase distortion by linear signal transforms

    F. Filbir, L. Liehr·Front. Appl. Math. Stat. 6Journal

  2. On the mathematical validity of the Higuchi method

    L. Liehr, P. Massopust·Phys. D 402Journal

Talks

Upcoming

2027

Past

2026
  • Online Analysis Research SeminarUniversity of Massachusetts Lowell, USA
    Oct 9, 2026
  • Phase Retrieval: Connecting Theory and ApplicationsRWTH Aachen, Germany
    Sep 21–25, 2026
2025
  • Zurich Colloquium in Applied and Computational MathematicsZurich, Switzerland
    Oct 8, 2025
  • Annual Meeting of the Israel Mathematical Union 2025, Analysis SessionIsrael
    Jul 6, 2025
  • Modern Trends in Fourier AnalysisBarcelona, Spain
    Jun 2–6, 2025
  • FIM Workshop on Phase Retrieval and Banach LatticesETH Zurich, Switzerland
    May 5–9, 2025
  • BIU Mathematics ColloquiumBar-Ilan University, Israel
    Mar 30, 2025
2024
  • ICMAT Research Term: Lattice Structures in Analysis and ApplicationsMadrid, Spain
    May 6–10, 2024
  • Workshop on Fourier Analysis and its ApplicationsBudapest, Hungary
    Jan 29 – Feb 2, 2024
2023
  • 11th Applied Inverse Problems ConferenceGöttingen, Germany
    Sep 4–8, 2023
  • Oberseminar Optimization and Data AnalysisTechnical University of Munich, Germany
    Jul 6, 2023
  • Mini-courses in Mathematical AnalysisPadova, Italy
    Jun 19–23, 2023
  • Workshop on Quantum Harmonic AnalysisNorwegian University of Science and Technology, Trondheim, Norway
    Jun 5–9, 2023
  • International Conference on Approximation Theory and BeyondVanderbilt University, Nashville, USA
    May 15–18, 2023
2022
  • Harmonic Analysis SeminarUniversity of Vienna, Austria
    Oct 17, 2022
  • 8th International Conference on Computational Harmonic AnalysisIngolstadt, Germany
    Sep 12–16, 2022
  • Curves and Surfaces ConferenceArcachon, France
    Jun 20–24, 2022
  • 11th International Conference on Harmonic Analysis and Partial Differential EquationsEl Escorial, Spain
    Jun 6–10, 2022