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Dr Daniel Hauer
School of Mathematics and Statistics F07
The University of Sydney, NSW 2006
Office: Carslaw Building Room 635
+61 2 862 70092
Fax: +61 2 9351 4534
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- Partial differential equations (PDEs)
- Eigenvalue problems and isoperimetric inequalities;
- Fundamental gap conjecture on manifolds;
- Regularity and qualitative properties of solutions to elliptic and parabolic PDEs;
- Maximum principles;
- Domain perturbation;
- Kurdyka-Łojasiewicz-Simon inequality and long-time asymptotic behaviour.
All PDEs I am studying usually involve the (local or fractional) p-Laplace operator, or doubly-nonlinear operators.
- Nonlinear harmonic analysis with applications to PDEs
- Regularity of nonlinear semigroups, gradient flows (in metric spaces);
- Fractional powers of (nonlinear) accretive operators;
- Dirichlet-to-Neumann operators and nonlinear Riesz operators;
- Interplay between semigroups and functional inequalities (Sobolev, Talagrand, etc.) .
- with Ben Andrews and Julie Clutterbuck, The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions, (2020).
- Daniel Hauer, Perturbation theory for homogeneous evolution equations, (2020).
- with Ben Andrews and Julie Clutterbuck, Non-concavity of the Robin ground state, Accepted for publication in Camb. J. Math., pages 1-69, (2020).
- with Thierry Coulhon, Regularisation effects of nonlinear semigroups - Theory and applications, Accepted for publication in BCAM Springer Briefs (2020).
- with Wolfgang Arendt, Maximal \(L^2\)-regularity in nonlinear gradient systems and perturbations of sublinear growth, Pure. Appl. Anal., Vol. 2, No. 1 (2020), Pages 23–34, DOI: 10.2140/paa.2020.2.23.
- MATH1001: 1st-year course on Differential Calculus in one and two real variables. I taught this course in sem. 1 of the years 2014-16;
- MATH1021 : 1nd-year course for Science students on Calculus of one variable . I am teaching this course in sem. 1, 2020;
- MATH2021 : 2nd-year course for Science students on Differential Equations and Vector Calculus . I taught this course in sem. 1 of the years 2018-19;
- MATH2067 : 2nd-year course for Science and engineering students on Differential Equations and Vector Calculus . I taught this course in sem. 1, 2017;
- MATH2917 : 2nd-year working seminar on Harmonic Analysis for students of the Special Studies Program. I taught this course in sem. 2, 2015;
- PMH4 : 4th-year course for Honours reading course on Advanced Measure Theory . I taught this course in sem. 2, 2015;
- MATH3068: 3rd-year course on Complex and Fourier Analysis. I taught this course in Sem. 2 of the years 2013-18;
- MATH3078, MATH3978/4078: 3rd-year mainstream and advanced students, and a 4th-year course on Partial Differential Equations and Waves. I taught this course in Sem. 2, 2019, and I will teach this course in sem. 2, 2020.
- Organiser of the AMSI/AustMS-event International Conference on PDEs, Geometric Analysis and Functional Inequalities from 7-10 March 2017 at the University of Sydney. This was jointly organised with Daniel Daners (USyd), Glen Wheeler (UoW) and Valentina Wheeler (UoW).
- Organiser of the AMSI/AustMS-event International conference on nonlinear partial differential equations from 21 – 25 November 2016 at the University of New England, Armidale . This was jointly organised with Florica Cirstea (USyd), Daniel Daners (USyd) and Yihong Du (UNE).
- Organiser of the AMSI-event Recent Trends in Nonlinear Evolution Equations from 4-5 November 2015 at the University of Sydney jointly with Valentina Wheeler (UoW). This workshop had the fundamental aim to showcase the recent advances on nonlinear evolution equations and to highlight key challenges for the future.
- Organiser of the AMSI-event
Analysis and PDE Seminar. This seminar day was organised jointly with the related research groups of the
- Australian National University,
- Macquarie University,
- University of Newcastle,
- University of New South Wales,
- University of Sydney,
- University of Wollongong ,
- Organiser of the seminar day WOMASY - Geometric and Harmonic Analysis meets PDE.
- Organiser of the seminar day WOMASY - Geometric and Harmonic Analysis meets PDE. This is a joint day of seminars
- Member of the nonlinear analysis group at the School of Mathematics and Statistics at the University of Sydney.
- Organiser of the University of Sydney PDE Seminar (jointly with Daniel Daners).