https://jakub-oprsal.info/etc/ Recent content in Etcs on jakub opršal Hugo -- gohugo.io en-gb Sun, 18 Oct 2026 12:11:14 +0200 https://jakub-oprsal.info/etc/ai/ Sun, 18 Oct 2026 12:11:14 +0200 https://jakub-oprsal.info/etc/ai/ For various reasons, including personal preference, ethical, and environmental, I do not use AI tools in my research. I make this statement without any prejudice on the work of my co-authors, and other colleagues. We are living through turbulent times, and it is not clear to see what the right coarse of actions is. I understand the pressure, in particular on younger colleagues, to publish more, and hence to use any enhancements that might give you an advantage. https://jakub-oprsal.info/etc/esslli/ Wed, 12 Aug 2026 09:00:00 +0200 https://jakub-oprsal.info/etc/esslli/ Algebraic approach to constraint satisfaction link to slides main theorem If there is a natural transformation $\operatorname{pol}(A) \to \operatorname{pol}(B)$ then $\operatorname{CSP}(B)$ reduces to $\operatorname{CSP}(A)$ in logspace. I recommend these two papers as an entry point into the theory. The first is recommended to anyone who knows what a functor is, and provides a categorical treatment of the above theorem. The second is more tradional. It was written for combinatorists, and provides a good overview of the state-of-the-art of the field just before the resolution of the dichotomy conjecture.