Computational complexity theory was born more than 50 years ago when researchers started asking themselves what could be computed efficiently. Classifying problems or functions with respect to the amount of resources (e.g. time and/or space) needed to solve or compute them turned out to be an extremely difficult question. This has led researchers to develop a remarkable variety of approaches, employing different mathematical methods and theories.

The future development of complexity theory will require a subtle understanding of the similarities, differences and limitations of the many current approaches. In fact, even though these approaches study the same phenomenon, they are developed today within disjoint communities, with little or no communication between them (e.g. algorithms, logic, programming theory, algebra etc.). This dispersion is unfortunate since it hinders the development of hybrid methods and more generally the advancement of computational complexity as a whole.

The goal (and peculiarity) of the Caleidoscope school is to reunite in a single event as many different takes on computational complexity as can reasonably be fit in one week.  It is intended for graduate students as well as established researchers who wish to learn more about neighboring areas.

The Caleidoscope school will be comprise of four main lecture courses, based on some of the most developed approaches to computational complexity today.

1. Boolean circuits and lower bounds. (Rahul Santhanam, University of Oxford).
2. Algebraic circuits and geometric complexity. (Peter Bürgisser, Technical University Berlin).
3. Proof complexity and bounded arithmetic; (Samuel Buss, University of California San Diego).
4. Machine-free complexity (descriptive and implicit complexity). (Anuj Dawar, University of Cambridge and Ugo Dal Lago, University of Bologna)

In addition to these broad-ranging themes, there will also be three more focussed topics, providing examples of (already established or potential) interactions between logic, algebra and complexity:

5. Constraint satisfaction problems. (Libor Barto, Charles University in Prague).
6. Communication complexity. (Sophie Laplante, Paris 7 University).
7. Duality in formal languages and logic. (Daniela Petrisan, Paris 7 University).

We believe that the advancement of research is best accomplished in an environment that is open, diverse and respectful to all participants. During the school, we will follow the anti-harassment policy of ACM.

Anupam Das (DIKU, University of Copenhagen)

Damiano Mazza (CNRS, LIPN, Université Paris 13)

Thomas Seiller (CNRS, LIPN, Université Paris 13)

Alexander Knop (University of California San Diego)