Prior to moving to Copenhagen and Lund, I worked at KTH Royal Institute of Technology as an assistant professor and then associate professor during the years 2011-2019. During 2008-2010 I was a postdoc at the Computer Science and Artificial Intelligence Laboratory at the Massachusetts Institute of Technology hosted by Madhu Sudan. Before that I was a PhD student of Johan Håstad in the Theory Group at KTH, where I defended my PhD thesis in May 2008. Please see my biographic sketch for more information.
Computers are everywhere today—at work, in our cars, in our living rooms, and even in our pockets—and have changed the world beyond our wildest imagination. Yet these marvellous devices are, at the core, amazingly simple and stupid: all they can do is to mechanically shuffle around zeros and ones. What is the true potential of such automated computational devices? And what are the limits of what can be done by mindless calculations? Understanding this kind of questions is ultimately what my research is about.
Computational complexity theory gives these deep and fascinating philosophical questions a crisp mathematical meaning. A computational problem is any task that is in principle amenable to being solved by a computer—i.e., it can be solved by mechanical application of mathematical steps. By constructing general, abstract models of computers we can study how to design efficient methods, or algorithms, for solving different tasks, but also prove mathematical theorems showing that some computational problems just cannot be solved efficiently for inherent reasons.
I am particularly interested in understanding combinatorial optimization problems, which are of fundamental mathematical importance but also have wide-ranging applications in industry. My goal is, one the one hand, to prove formally that many such problems are beyond the reach of current algorithmic techniques, but also, on the other hand, to develop new algorithms that have the potential to go significantly beyond the current state of the art. Recently, I have also been doing research on how complexity theory can be harnessed to produce certificates that algorithms are actually computing correct results. It is an open secret in combinatorial optimization that even the best commercial tools sometimes produce wrong answers, but there has been no really principled way of addressing this problem. We are working on changing this. See the presentation of my research group for a slightly more detailed description.