About me
I am a Van Vleck Visiting Assistant Professor at the University of WisconsinMadison. I study nonlinear partial differential equations, in particular those arising in the study of fluid dynamics.
Recently I also spent a year as a Simons Postdoctoral Fellow at the University of Cambridge and at the Isaac Newton Institute for Mathematical Sciences. I completed my PhD working with Ian Tice at Carnegie Mellon University. The beginning of my mathematical history can be traced back to the University of Warwick where I carried out my undergraduate studies.
Research interests
I work on nonlinear partial differential equations. I am particularly interested in free boundary problems, geophysical flows, and complex fluids.
Free boundary problems
Many important physical processes occur at interfaces and they are often challenging to describe mathematically. In particular I am interested in the stability of viscous surface waves (see here), studying ferrofluids or the effects of surfactants (here's a fun example of what surfactants can allow you to do: 'soappowered' boat races!)
Geophysical flows
Ranging from local weather prediction to longterm climate models, the various scales of interest in geophysical flows require an assorted array of mathematical models. In collaboration with Leslie Smith and Sam Stechmann I am currently working on the role of moisture in atmospheric models, where the incorporation of moisture means additional physical processes to consider as well as the introduction of phase boundaries (such as aircloud interfaces).
Micropolar fluids
Many everyday fluids, such as milk, blood, or liquid crystals (ubiquitous in the electronic displays that surround us) are socalled "complex fluids". This means that they are fluids in which microstructure is present (typically at the microscopic scale) which impacts the overall behaviour of the fluid. More precisely, in these examples, the microstructure corresponds to the fat molecules in milk, the hemoglobin in blood, and the constituting molecules of the liquid crystal themselves.
For a mathematicianfriendly introduction to micropolar fluids (i.e. written in mathematical language rather than engineering parlance), see the first chapter of my doctoral thesis. In joint work with Ian Tice we studied the stability of rodlike and pancakelike microstructure (see here and here).
Publications
Preprints
 A. RemondTiedrez, L. M. Smith, and S. N. Stechmann, A nonlinear elliptic PDE from atmospheric science: wellposedness and regularity at cloud edge [ arxiv, pdf ]
To appear
 A. RemondTiedrez and I. Tice, Anisotropic micropolar fluids subject to a uniform microtorque: the stable case, Analysis & PDE [ arxiv, pdf ]
Published
 A. RemondTiedrez and I. Tice, Anisotropic micropolar fluids subject to a uniform microtorque: the unstable case, Communications in Mathematical Physics (2021) [ arxiv, journal, pdf ]
 A. RemondTiedrez and I. Tice, The viscous surface wave problem with generalized surface energies, SIAM Journal on Mathematical Analysis (2019) [ arxiv, journal, pdf ]
Thesis
 A. RemondTiedrez, Nonlinear partial differential equations in fluid dynamics: interfaces, microstructure, and stability ( pdf ). The first chapter of this thesis is a selfcontained introduction to micropolar fluids, including a derivation of their equations of motion.
Talks
 December 2023: Arizona State University, PDE Seminar (Moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries) [ slides ]
 October 2022: University of Cambridge, PDE Seminar (Moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries) [ slides ]
 May 2022: Carnegie Mellon University, Center for Nonlinear Analysis Seminar (Moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries) [ slides, recording ]
 May 2022: Isaac Newton Institute, Junior Isaac Newton Crossover (JINX) Seminar (Instability of an Anisotropic Micropolar Fluid) [ slides, recording ]
 Apr. 2022: Twelfth IMACS International Conference on Nonlinear Evolution Equations, Athens (GA) (Instability of an Anisotropic Micropolar Fluid) [slides]
 Mar. 2022: Isaac Newton Institute, programme on the mathematical aspects of turbulence (Moist potential vorticity inversion: a nonlinear PDE from atmospheric dynamics with free boundaries) [slides]
 Nov. 2021: Texas A&M University, Nonlinear PDE Seminar (Variational formulation, wellposedness, and iterative methods for moist potential vorticity inversion: a nonlinear elliptic PDE from atmospheric dynamics with free boundaries) [slides]
 Oct. 2021: University of WisconsinMadison, PDE and Geometric Analysis Seminar (Variational formulation, wellposedness, and iterative methods for moist potential vorticity inversion: a nonlinear elliptic PDE from atmospheric dynamics with free boundaries) [slides]
 May 2021: Ohio River Analysis Meeting, Lexington (Instability of an anisotropic micropolar fluid) [slides]
 Feb. 2021: University of WisconsinMadison, Applied and Computational Mathematics Seminar (Instability of an anisotropic micropolar fluid) [slides]
 Oct. 2020: University of Southern California, Analysis and PDE Seminar (Instability of an anisotropic micropolar fluid) [slides]
 May 2020: Online North East PDE and Analysis Seminar (jointly organized by Brown, Carnegie Mellon, Princeton, and Toronto) (Instability of an anisotropic micropolar fluid) [slides]
 Dec. 2019: SIAM Conference on Analysis of Partial Differential Equations, La Quinta (Instability of a nonisotropic micropolar fluid) [slides]
 Jul. 2019: Equadiff, Leiden (The viscous wave problem with generalized surface energies) [slides]
 Feb. 2019: SIAM Conference on Computational Science and Engineering, Spokane (Viscous surface waves with generalized surface energies) [slides]
 Apr. 2018: Graduate Student Seminar MiniConference, Carnegie Mellon University (Decay of surface waves) [slides]
 May 2017: Summer School on Mathematical Fluids, University of Southern California (Viscous surface waves and their stability) [slides]
Mentoring
Fall 2021: Directed Reading Program
 The Directed Reading Program pairs undergraduate students with mentors that guide the students through readings on a topic of mutual interest for the duration of a semester. In the fall 2021 I supervised David Kwak reading about the Calculus of Variations, following notes by Peter Olver.
Teaching
Spring 2024

This spring I am teaching linear algebra (MATH 341).
This course aims to introduce students to the fundamental concepts of linear algebra and,
simultaneously, develop their proofwriting skills.
Lecture notes from previous courses
Contact
Email: aremondtiedrezatmathdotwiscdotedu
Office: Van Vleck 607