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About the School

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General Information

Dr Daniel Hauer
Academic Fellow
School of Mathematics and Statistics F07
The University of Sydney, NSW 2006
Australia
 
Office: Carslaw Building Room 635
Phone:
+61 2 862 70092
Fax: +61 2 9351 4534
See Profile on Google Scholar

Research Interests

  • 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.) .

Recently Submitted Papers

Recently Accepted Papers

Teaching

  • 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.

Professional Activities

  • 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.