Currently, most of my research effort aims at a project on computational homotopy theory.
Homotopy theory studies geometric phenomena robust in a certain strong sense. It is an old area of mathematics with many surprising connections. Largely, it is built in a non-constructive fashion and that is a substantial obstacle to be overcome when one works towards its computational applications.
In a series of papers we made some of the crucial homotopy-theoretic elements algorithmic.
For a brief visual introduction, see the SODA 2012 slides. For slightly more involved visual exposition, you can try ATMCS 2012 slides. For a complete exposition of the main result, see Computing all maps into a sphere.
Also other directions of my research interests belong to theoretical computer science. Mainly, it is linear programming and its applications in algorithm design.
Teaching/Pro studenty (In Czech)
My tutorials aim at three goals:
- Put emphasis on the visual component in my presentation (pictures, colored chalks, etc.).
- Provide essential portion of time for individual work of students (interaction of students is not excluded).
- Assign, correct and comment regular homework (interconnected with the lecture if possible).
A simple but, in my opinion, handy technical solution can be seen at particular courses accessible from the Teaching page (in Czech but essentially comprehensible).
I often find math papers (of the standard TeX/LaTeX style) uneasy to understand and remember. They mostly involve text/language skills and memory, while my (mathematical) mind "works in pictures" from a great part.
I believe significant portion of math-readers would benefit from stronger visual component in math exposition. A couple of my experiments with IPE (a graphical tool for math pictures, handouts and slides) in this direction can be found at my Exposition page.
- Technology - particularly high-tech phones; My own creativity peaked with the development of a dictionary for phones with Java.
- Sports - I am a big fan of sporting for fun, welcoming beginners is more important to me than competitive ambitions.