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Property testing: A topic in which I am very involved in the last years. Basically this deals with an approximation notion that for many problems allows for the construction algorithms that can resolve it without reading the entire input, and many times have a correspondingly sublinear running time. This is a relatively young topic that is still growing.
Graph theory: Mathematically speaking I grew up on graph theory, as my publications from the time of my Ph.D. studies would confirm. I am still very interested in this topic, and especially in applications of the Regularity Lemma. I am also interested in applications of combinatorial theory, and graph theory in particular, to property testing, logic (see below), and computational theory in general.
Formal logic and finite model theory: This is an exciting field that has a lot in common with combinatorial theory. It basically deals with asking what structures can be easily described, and what properties can be easily calculated, within a given language and under a given set of restrictions.
Probabilistically Checkable Proofs: As the name suggests, this deals with proof protocols that are easy (in that they take only a few queries) to verify, though the theory of constructing such proofs is not easy at all. In essence the existence of an easy to verify proof may mean that a certain approximation problem is hard, because such a proof may serve as a reduction to an NP-Hard problem. This has some connections with property testing, since a verification of a proof can start with a property test for a feature that once guaranteed makes the proof easier to verify.
Other topics in computational theory and combinatorics: The above list of course does not exclude other topics from catching my attention. In particular, I have also some interests in statistical deduction algorithms, coding theory, and database query evaluation algorithms.
During the year 2012-2013 I will probably be on a teaching break. I'll update here in case this changes.
Every year (from 2002-2003) I'm giving the course Probabilistic Methods and Algorithms; it has undergone a major upgrade in 2011 and is now a three point course.
In the 2009 Spring semester and the 2010-2011 winter I tried something new, an advanced seminar revolving around the reading and analysis of a hard research paper(s). I intend to give this seminar again; take a look at the last time to see if you're interested.
Starting in 2002 I gave almost every year a property testing seminar. It will probably be put on hold for a few years now, unless I receive sufficiently many requests to hold it again.
I have taught the course Database management systems (236363) from 2004, and will continue to teach it in the future.
I have managed (but not taught) Introduction to computing (234112) in the 2008-2009 Winter semester.
I have also given the course File systems (234322) in the 2003 Spring semester.