Research interests
As an undergraduate student I got tangled up with liquid crystals and knotted fields under the supervision of Gareth Alexander. Now as a graduate student I am juggling epsilons and deltas, and am interested in applying tools from mathematical analysis to questions inspired by the physical sciences. In particular, under the supervision of Ian Tice, I am currently working on free-boundary problems arising from fluid mechanics.
More precisely, I work on nonlinear partial differential equations. I am particularly interested in the nonlinear stability analysis of viscous surface waves and complex fluids, studying ferrofluids or the effects of surfactants (here's a fun example of what surfactants can allow you to do: 'soap-powered' boat races!)
I am also interested in micropolar fluids, which are fluids in which a microstructure is present (typically at the microscopic scale) which impacts the overall dynamics of the fluid. For example, milk, blood, and liquid crystals are all micropolar fluids, where the microstructure corresponds to the fat molecules in milk, the hemoglobin in blood, and the constituting molecules of the liquid crystal themselves.
Talks
- Dec. 2019: Instability of a non-isotropic micropolar fluid (SIAM Conference on Analysis of Partial Differential Equations, La Quinta) [slides]
- Jul. 2019: The viscous wave problem with generalized surface energies (Equadiff, Leiden) [slides]
- Feb. 2019: Viscous surface waves with generalized surface energies (SIAM Conference on Computational Science and Engineering, Spokane) [slides]
- Apr. 2018: Decay of surface waves (Graduate Student Seminar Mini-Conference, Carnegie Mellon University) [slides]
- May 2017: Viscous surface waves and their stability (Summer School on Mathematical Fluids, University of Southern California) [slides]
Teaching
Spring 2020: Linear algebra
This semester I am a TA for 21-241 Matrices and Linear Transformations. Below you will find notes used for recitations.Recitation notes: Jan 14, 21.
Fall 2019: Concepts of Mathematics
Last semester I was a TA for 21-127 Concepts of Mathematics. Below you will find notes used for recitations as well as feedback regarding mistakes commonly made on homework problems.Recitation notes: Aug 29, Sep 03, 05, 10, 12, 17, 19, 24, Oct 01, 03, 08, 10, 15, 17, 22, 29, 31, Nov 05, 07, 12, 19, 21, 26, Dec 03.
Feedback: HW 1, HW 2, HW 3, HW 4, HW 5, HW 6, HW 7, HW 8, HW 9.
Summer 2018: Concepts of Mathematics
(click here for the course website)
In the summer of 2018 I taught "Concepts of Mathematics" to high school students participating in the Advanced Placement / Early Admission (AP/EA) program. All material from the course has been collected into four (rather bulky) files: lecture notes, quizzes, HW, and tests, as well as into one (even bulkier) single file.Extra material: Due to popular demand, here are notes and HW problems (with solutions) from last year's portion of the course dedicated to the study of sequences and their convergence.
SIAM Student Chapter
I have been involved with the SIAM Student Chapter at CMU for the past four years, and most recently have been serving as President since 2018. During my time here we have begun running 'working groups' every semester where we (mathematics graduate students) get together to study in detail a particular topic. We attempt to pick topics living in that sweet spot between graduate level textbooks and current research topics. Amongst the topics we studied somewhat recently, I must admit that my personal favourites are either related to geometry or fluid dynamics, namely 'geometric measure theory', 'calculus of variations on manifolds and geometric flows' (which consisted mostly in the study of mean curvature flow), and 'analysis of hydrodynamical models'.
The full list of working groups can be found on the SIAM Student Chapter's webpage.
Contact
Email: aremondt-at-andrew-dot-cmu-dot-edu
Office: Wean Hall 7106