Duality in Computer Science

Summary

Aims of the seminar

Duality allows one to move between an algebraic world of properties and a spacial world of individuals and their dynamics, thereby leading to a change of perspective that may, and often does, lead to new insights. Because computer science is fundamentally concerned both with specification of programs and the dynamics of their executions, dualities have given rise to active research in a number of areas of theoretical computer science. In this seminar we particularly wanted to concentrate on applications of duality in semantics for continuous data with special focus on probability in computation, algebra and coalgebra, and applications in complexity theory.

The seminar

Our call for participation was exceptionally successful and right up to the actual start of the meeting we were in danger of exceeding the number of places allocated. We see this as a vindication of our aim of bringing these researchers together for exchanging ideas centred around the common topic of duality. The talks offered fell quite naturally into groupings which allowed us to adopt a fairly thematic programme structure:

• Day 1, morning session: Duality and classical algebra. Talks by Libor Barto, Michael Pinsker, Max Dickmann, and Marcus Tressl.
• Day 1, afternoon session: Duality and categories. Talks by Paul Taylor, Steve Vickers, and Pino Rosolini.
• Day 2, morning session: Duality and topology. Talks by Matthew de Brecht, Mathias Schröder, Reinhold Heckmann, and Jean Goubault-Larrecq.
• Day 2, afternoon session: Alternative views on duality. Talks by Niels Schwartz, George Hansoul, Rob Myers, and Alexander Kurz.
• Day 3, morning session: Duality and coalgebra. Talks by Adriana Balan, Dirk Pattinson, Ulrich Berger, and Samuel J. van Gool.
• Day 4, morning session: Duality and domain theory. Talks by Jimmie Lawson, Abbas Edalat, Achim Jung, and Klaus Keimel.
• Day 4, afternoon session: Duality and logic. Talks by Peter Schuster, Martín Escardé, Vladimir Shavrukov, and Vasco Brattka.
• Day 5, morning session: Duality and probability. Talks by Willem Fouché, Dexter Kozen, Daniela Petric san, and Drew Moshier.

Final thoughts

As always, Dagstuhl staff were incredibly efficient and helpful which allowed all of us, including the organisers, to focus on the exchange of ideas and plans for joint work. We are sincerely grateful to them for their hospitality and professionalism.

Mai Gehrke (LIAFA, CNRS and University Paris Diderot)
Achim Jung (School of Computer Science, University of Birmingham)
Victor Selivanov (Institute of Informatics Systems, RAS, Novosibirsk)
Dieter Spreen (Math. Logik und Theoretische Informatik, Universität Siegen)