My hometown. Here I was born in 1983, here I grew up and studied mathematics, and now I'm working at one of the two major universities here. In Wrocław I met my wife Agata, in fact we grew up in the same street. Wrocław is likely a nice city to live in, and with no doubt a great place to visit. You may have heard about the Market Square, Ostrów Tumski, the Racławice Panorama and Hala Stulecia. But did you know about the double staircase at Teatralna 1, a fancy Archicom building or birds you can spot in Wrocław?
In 2008 I got a PhD degree in mathematics under the supervision of Tadeusz Kulczycki, and since then I work as an assistant professor at the Wrocław University of Technology. In 2010–2012 I also held a temporary position at the Polish Academy of Sciences. My main fields of interest are:
- Lévy processes and half-line. Fluctuation theory for Lévy processes is an infinite source of identities for stopping times, supremum processes, ladder processes etc. However, a formula for the eigenfunctions or transition density of the process killed after exiting a half-line seems to be out of reach of this theory. I managed to obtain such results using purely analytical methods for a class of Lévy processes. Extending this to a wider class of processes, and studying the relation between eigenfunctions and fluctuation identites are the plans for my nearest future.
- Potential theory of Markov processes with jumps. Typically, the theory of jump processes is considered to be more difficult than its diffusion counterpart, mostly due to issues related to nonlocality. The generalization of methods of classical potential theory (related to Brownian motion) to the case of processes with jumps often requires considerable effort. Fortunately, sometimes jumps help! My research is focused on these two words.