Daan Michiels

I'm a graduate student in mathematics at the University of Illinois at Urbana-Champaign in the US. Most of the math I do has a geometrical or topological flavor to it. That's because I like pictures.

You can contact me at michiel2@illinois.edu.

Occasionally, you can find me on Mathematics StackExchange or on MathOverflow.

Teaching

I am currently a teaching assistant for Math 241, Calculus III (merit section).

In Spring 2017, I was a teaching assistant for Math 285, Introduction to Differential Equations (merit section).

In Fall 2016, I was a teaching assistant for Math 231, Calculus II (merit section).

In Fall 2014, I was a teaching assistant for Math 241, Calculus III (merit section).

In Spring 2014, I was a teaching assistant for Math 415, Applied Linear Algebra.

In Fall 2013, I was a teaching assistant for Math 241, Calculus III.

Illinois Geometry Lab

Since Spring 2017, I have been a team leader for the Visual Cliffs, Virtual Reality and Movement Disorders project at the Illinois Geometry Lab.

In Fall 2016, I was a team leader for the Business Analytics project at the Illinois Geometry Lab.

In Fall 2014 I was the team leader of the project Hyperbolic Space on the Oculus Rift. The project continued in Spring 2015. The code is available on github.

In Spring 2014 I was the team leader of the Orbifolds project. The goal of this project was to visualize good 2-dimensional orbifolds whose universal cover is the plane. We did this directly in the web browser, and the result can be found here (recent webbrowser required; in my experience Chrome works best).

Master's thesis

As part of my master's degree at the University of Leuven (Belgium), I wrote a thesis called Moduli Spaces of Flat Connections. You can download it as a pdf-document.
There is also a condensed version available of the slideshow I used for my thesis defense. This pdf-document is the original slideshow without animation and with only one overview slide.

Visualizing Frenet-Serret

I once made a visualization of the Frenet-Serret frame of a curve in differential geometry. You can download it as a video here.
The video shows a space curve in red (twice continuously differentiable). An airplane follows the curve at unit speed, orienting itself according to the Frenet frame. The nose points along the tangent and the 'up' direction of the plane points along the normal, so that the right wing points along the binormal. The curvature can then be interpreted as the pitch of the plane, and the torsion as rolling. Someday I should add curvature and torsion to the animation.
The animation was made in Blender. Thanks go to Pieter Segaert for rendering some of the frames on his computer.

Other documents

In March of 2013, I taught a session on inequalities to several excellent participants of the Flemish Mathematical Olympiad, as preparation for the International Mathematical Olympiad. The notes I wrote up are available as a pdf-document. They are in Dutch.

How many strings of six letters contain no letter more than twice? The answer is provided here in Dutch.

In the summer of 2012 I started a project called Egel (Dutch for hedgehog; no reason) to help students pass the Belgian entrance exam for medical school. The project is no longer online, but I've tried to make a usable offline version. You can now find the project here, packed as a zip file. Unzip it, and open index.html in your web browser. Almost everything should work without problems. Oh, by the way, it's in Dutch.