Mathematicians think I am a computer scientist, computer scientists think I am a mathematician. And I think I am a barber.
My work lies at the interface of mathematics and computer science. I am seeking to answer what inherent mathematical quality makes a computational problem hard, and which allows us to design an efficient algorithm to solve this problem. In essence, we are asking if P ≠ NP, how can we distinguish problems that are in P from those that are NP-complete?
To answer these questions, I investigate the complexity of constraint satisfaction problems and its variants including approximation. To study those I use deep mathematical theories, including topology, topological combinatorics, and universal algebra.
accademic positions and long-term visits
- since Jun 2022 IST-Bridge Fellow, ISTA, Klosterneuburg, Austria. Joining Uli Wagner’s group with my project ‘Topology and the complexity of approximate graph colouring’ supported by the Marie Skłodowska-Curie Action, Grant Agreement No. 101034413.
- 2021–2022 Post-doc, University of Oxford, UK. Working with Standa Živný on his ERC grant ‘PowAlgDO’.
- Apr–May 2019 Research stay at Carnegie Mellon University, US. Visiting Venkat Guruswami.
- 2018-2021 Post-doc, Durham University, UK. Working with Andrei Krokhin.
- 2016–2018 Post-doc, Technische Universität Dresden, Germany. Employed on Manuel Bodirsky’s ERC grant ‘CSP-Infinity’.
- Mar–Sep 2016 Post-doc, Jagellonian University, Kraków, Poland. Working with Marcin Kozik.
- Jun–Dec 2013 Research stay at Johannes Kepler University, Linz, Austria.
- 29 Feb 2016 Mathematics, Charles University in Prague, Czech Republic. thesis: Relational approach to universal algebra advised by Libor Barto
- 2009–2015 Charles University in Prague. Linear algebra, Elementar number theory, Algebra, Universal algebra for Mathematics students, Algebra for computer science students.
- 2009–2011 Czech Technical University, Prague. Linear algebra for engineering students.
- 2006–2009 Part of organization team of a correspondence mathematical competition for high school students Matematický korespondenční seminář.
- An introduction to promise CSP, free structures, and minions, Dagstuhl Seminar 22201, 16 May 2022.
- Promises, constraint satisfaction, and problems: Beyond universal algebra, AAA 100, 6–7 Feb 2021. (slides/part i) (part ii)
- The future of promises, CSP World Congress 2020, Völs am Schlern, IT, 21 Sep 2020.
- Promise constraint satisfaction, SSAOS, Špindlerův mlýn, Czech Republic, 4 Sep 2018. (slides)
- Blockers of linear Mal’cev conditions, First Algebra Week, Sienna, Italy, 20 Jun 2018.