ALGACOM
Starting from the 1st of September, 2024 I am working on my Marie Skłodowska-Curie project ALGACOM, which stands for Algorithms and Game Comonads.
A brief description of this project:
Our modern society is driven by computers, digital services, and algorithms. Understanding their weaknesses and limitations is one of the main subjects of study of theoretical computer science. Probably the most studied aspect of algorithms is their efficiency of use of computational resources, embodied as the running time of an algorithm. Parameterised complexity is a branch of theoretical computer science interested in determining whether there exists an efficient algorithm that solves a given computational problem. The efficiency is determined based on the structure of the input data.
The main limitation of parameterised complexity is that these analyses of computational problems are done on a case-by-case basis. This means that if somebody changes the problem or its parameterisation ever so slightly, the whole analysis has to be redone from scratch.
To tackle this problem we propose to use game comonads, a novel structural approach to logic in computer science. The theory of game comonads draws its strength from category theory, a well-established discipline of mathematics which specialises on compositionality, reusability of its tools and high-level of abstraction. Game comonads, despite being relatively new, have already shown to be a useful tool in the study of finite model theory, which is an adjacent area of study of parameterised complexity.
The primary goal of this project is to bring compositional tools of category theory into the setting of algorithms, with game comonads acting as the connecting glue. This project bring together expertise in category theory, in the form of the applicant and expertise in parameterised complexity, in the form of the host institution and the supervisor who will devote their efforts into bridging the gap between the two thus-far mostly disjoint disciplines of computer science and mathematics.
Project activity
- 8-13 Sep 2024: Presented an invited talk at the Summer School on General Algebra and Ordered Sets.
- 15 Oct 2024: Submitted an ERC Starting proposal (✔️).
- since 17 Oct 2024: supervising an undergraduate project (✔️).
- 21 Oct 2024: Introduced my project at the local GGOAT seminar (✔️).
- 23 Jan 2025: Submitted a preprint on Constraint Satisfaction and Category Theory with Max Hadek and Jakub Opršal.
- 11 Mar 2025: Attended the grant writing training at the CTU (✔️).
- 3 April 2025: Submitted a GACR grant (✔️).
Remark: Activities marked with (✔️) were promised in my MSCA project proposal.
Acknowledgement
The project is funded by the EU’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101111373. The supervisor is Dušan Knop. 
The website reflects only the view of the project ALGACOM. Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or Czech Technical University. Neither the European Union nor the granting authority can be held responsible for them.