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General Information


Dr Daniel Hauer
Senior Lecturer
School of Mathematics and Statistics
The University of Sydney, NSW 2006
Australia
 
Office: Carslaw Building, Room 635
Phone:
+61 2 862 70092
Fax: +61 2 9351 4534
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Research Interests

In the mathematical research, I intend to improve the general understanding and to broaden the current knowledge of various modern topics in mathematical analysis , including application to (stochastic) partial differential equations and mathematical physics.
In my work, I enjoy using different perspectives and approaches to study and to develop solutions to current important mathematical problems. For this, I don't hesitate using abstract views from functional analysis, microscopic views by using tools from stochastic analysis, and optimal transportation.
More precisely, I regularly contribute to the following topics.
  • Eigenvalue problems and isoperimetric inequalities with main focus on the Fundamental gap conjecture for Schrödinger operators
  • Calculus of variation with application to PDEs
  • Regularity theory in nonlinear Evolution problems
  • Non-existence and long-time stability in nonlinear Evolution problems
  • Homogenization and domain perturbation
  • Stochastic analysis with application to stochastic (partial) differential equations
  • Optimal Transportation

Recently Submitted Papers

  • [P1] with David Lee, Functional Calculus via the extension technique: a first hitting time approach, available on ArXiv: 2101.11305 , (2021).
  • [P2] with J. Mazón, The Dirichlet-to-Neumann operator for functions of least gradient and associated diffusion problems, available on ArXiv: 1910.12219 , (2021).

Recently Accepted Papers

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Teaching

  • MATH1001: 1st-year course on Differential Calculus in one and two real variables. I taught this course in Semester 1 of the years 2014-16;
  • MATH1021 : 1nd-year course for Science students on Calculus of one variable . I taught this course in Semester 1 of the years 2020 and 2021;
  • MATH2021 : 2nd-year course for Science students on Differential Equations and Vector Calculus . I taught this course in Semester 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 Semester 1, 2017;
  • MATH2917 : 2nd-year working seminar on Harmonic Analysis for students of the Special Studies Program. I taught this course in Semester 2, 2015;
  • PMH4 : 4th-year course for Honours reading course on Advanced Measure Theory . I taught this course in Semester 2, 2015;
  • MATH3068: 3rd-year course on Complex and Fourier Analysis. I taught this course in Semester 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 Semester 2, 2019 and 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.