Fredrik H𝕚ldrum
About
Mathematical research
- Existence theory and properties of travelling waves for nonlinear and nonlocal dispersive evolution equations; in particular, for Whitham-type equations.
- Regularisation theory for inverse problems.
Working in the research group of
Professor Mats Ehrnström.
Teaching
- Fall 2022: Lecturer ("interactive lectures") in
TMA4100 - Mathematics 1 - Single variable calculus - Spring 2023: Coordinator and lecturer in
TMA4115 - Mathematics 3 - Linear algebra
Preprints
- Subgradient-based Lavrentiev regularisation of monotone ill-posed problems.
With Markus Grasmair. arXiv:2005.08917.
Publications
- Periodic Hölder waves in a class of negative-order dispersive equations.
Journal of Differential Equations, 2023, 343, 752–789.
With Jun Xue. arXiv:2202.07363. - Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity.
Nonlinearity, 2020, 33 (4), 1594–1624. arXiv:1903.03354.
Academic degrees
- PhD in Mathematics at NTNU (2022) on
- Nonlocal and monotone techniques in dispersive equations and inverse problems.
- Supervisor: Mats Ehrnström; co-supervisor: Markus Grasmair.
- Integrated (5-year) MSc in Applied Physics and Mathematics with specialization in Industrial Mathematics at NTNU (2016).
- Thesis: On the Existence of Periodic Traveling Waves to the Whitham Equation.
- Project: Optimal Control of Elliptic Partial Differential Equations.
- BSc in Mathematical Sciences with specialization in Mathematics at NTNU (2016). Project: Introduction to Isogeometric Analysis.
Publications
2025
-
Grasmair, Markus;
Hildrum, Fredrik.
(2025)
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems.
Inverse Problems
Academic article
2023
-
Hildrum, Fredrik;
Xue, Jun.
(2023)
Periodic Hölder waves in a class of negative-order dispersive equations.
Journal of Differential Equations
Academic article
2020
-
Hildrum, Fredrik.
(2020)
Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity.
Nonlinearity
Academic article
Journal publications
-
Grasmair, Markus;
Hildrum, Fredrik.
(2025)
Subgradient-based Lavrentiev regularisation of monotone ill-posed problems.
Inverse Problems
Academic article
-
Hildrum, Fredrik;
Xue, Jun.
(2023)
Periodic Hölder waves in a class of negative-order dispersive equations.
Journal of Differential Equations
Academic article
-
Hildrum, Fredrik.
(2020)
Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity.
Nonlinearity
Academic article
Teaching
Fall 2024:
Fall 2023:
- Coordinator in TMA4110 - Mathematics 3 - Linear algebra
- Lecturer in TMA4100 - Mathematics 1 - Single variable calculus (5 two-hour lectures a week)
Spring 2023:
- Coordinator and lecturer in TMA4115 - Mathematics 3 - Linear algebra
Fall 2022:
Outreach
2024
-
Academic lectureHildrum, Fredrik. (2024) Existence and properties in water-wave models. University of Oslo Norwegian meeting on PDEs 2024 , Oslo 2024-06-05 - 2024-06-07
2023
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Academic lectureHildrum, Fredrik. (2023) Periodic Hölder waves in a class of negative-order fKdV-like equations. Dispersive seminar (UiB, Lund University and NTNU) 2023-02-14 - 2023-02-14
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Academic lectureHildrum, Fredrik. (2023) Periodic Holder waves in a class of negative-order dispersive equations. The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications , Wilmington, NC 2023-05-31 - 2023-06-04
2022
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Academic lectureHildrum, Fredrik. (2022) Periodic Hölder waves in a class of negative-order dispersive equations. 28th Nordic Congress of Mathematicians , Aalto University 2022-08-18 - 2022-08-21
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Academic lectureHildrum, Fredrik. (2022) Total variation-based Lavrentiev regularisation of monotone problems. 10th International Conference "Inverse Problems: Modeling and Simulation" 2022-05-22 - 2022-05-28
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Academic lectureHildrum, Fredrik. (2022) Periodic Hölder waves in nonsmooth fractional KdV equations. Institutt for matematiske fag, NTNU The DNA Seminar , Trondheim 2022-03-28 - 2022-03-28
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Academic lectureHildrum, Fredrik. (2022) Large-amplitude traveling waves with exact Hölder regularity in negative-order fKdV equations. SIAM SIAM 2022 Conference on Analysis of Partial Differential Equations (PD22) , Virtual (Berlin) 2022-03-14 - 2022-03-18
2019
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PosterHildrum, Fredrik. (2019) Existence of traveling waves in nonlinear dispersive equations of Whitham-type. Norwegian meeting on PDEs 2019 , Trondheim 2019-06-05 - 2019-06-07
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Academic lectureHildrum, Fredrik. (2019) Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity. Lunds Universitet, Matematikcentrum, Analysis/PDE seminar , Matematikcentrum, Lunds Universitet 2019-03-26 -
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Academic lectureHildrum, Fredrik. (2019) Nonlinear Lavrentiev regularization of monotone ill-posed equations. Inverse Days 2019 , Paviljonki conference center, Jyväskylä 2019-12-16 - 2019-12-18
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Academic lectureHildrum, Fredrik. (2019) Nonlinear Lavrentiev regularization of monotone ill-posed equations. Chemnitz Symposium on Inverse Problems 2019 , Frankfurt 2019-09-30 - 2019-10-02
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Academic lectureHildrum, Fredrik. (2019) Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity. The Eleventh IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory , University of Georgia, Athens, GA 2019-04-17 - 2019-04-19
2018
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LectureHildrum, Fredrik. (2018) 1) Regularization of ill-posed problems & 2) Existence of traveling waves in nonlinear dispersive equations. Nasjonalt matematikermøte , Bergen 2018-09-12 - 2018-09-14
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PosterHildrum, Fredrik. (2018) Existence of traveling waves in nonlinear dispersive equations of Whitham-type. Lund Workshop on Fluid Dynamics and Dispersive Equations , Lund University 2018-06-25 - 2018-06-29
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PosterHildrum, Fredrik. (2018) Denoising piecewise constant signals in first-kind Volterra equations. 9th International Conference "Inverse Problems: Modeling and Simulation" 2018-05-21 - 2018-05-25
2016
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Popular scientific lectureHildrum, Fredrik. (2016) On a Mathematical Model for Water Waves. NTNU, NorMathsIn and ECMI Math Meets Industry – What can you do with a PhD? , Trondheim 2016-09-22 - 2016-09-23