Fredrik Hildrum
Om
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.
Undervisning
Emner
Formidling
2023
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Vitenskapelig foredragHildrum, 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.
2022
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Vitenskapelig foredragHildrum, Fredrik. (2022) Large-amplitude traveling waves with exact Hölder regularity in negative-order fKdV equations. SIAM 2022 Conference on Analysis of Partial Differential Equations (PD22) . SIAM; Virtual (Berlin). 2022-03-14 - 2022-03-18.
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Vitenskapelig foredragHildrum, 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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Vitenskapelig foredragHildrum, Fredrik. (2022) Periodic Hölder waves in nonsmooth fractional KdV equations. The DNA Seminar . Institutt for matematiske fag, NTNU; Trondheim. 2022-03-28 - 2022-03-28.
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Vitenskapelig foredragHildrum, Fredrik. (2022) Total variation-based Lavrentiev regularisation of monotone problems. 10th International Conference "Inverse Problems: Modeling and Simulation" ; 2022-05-22 - 2022-05-28.
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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Vitenskapelig foredragHildrum, 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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Vitenskapelig foredragHildrum, 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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Vitenskapelig foredragHildrum, 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.
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Vitenskapelig foredragHildrum, 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.
2018
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Faglig foredragHildrum, 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) Denoising piecewise constant signals in first-kind Volterra equations. 9th International Conference "Inverse Problems: Modeling and Simulation" ; 2018-05-21 - 2018-05-25.
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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.
2016
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Populærvitenskapelig foredragHildrum, Fredrik. (2016) On a Mathematical Model for Water Waves. Math Meets Industry – What can you do with a PhD? . NTNU, NorMathsIn and ECMI; Trondheim. 2016-09-22 - 2016-09-23.