Report on DMTCS'96 (by Marjo Lipponen)

The first conference of a planned series of conferences was organized by the Centre for Discrete Mathematics and Theoretical Computer Science at the University of Auckland. The aim of the conferences is to link mathematics and computing.

Auckland, the "city of sails", has a population close to one million. It is antipodal to Athens, with sub-tropical climate. December corresponds to the start of the summer holiday period in New Zealand, which was a very welcome break for us who came from the nothern hemisphere. Weather was fine (above 20 degrees) most of the time but we also experienced quick changes to showers and thunder. A hint of Christmas was given by pohutukawas, New Zealand Christmas trees with their beautiful red flowers. The city campus is situated on a rise overlooking the harbour, five-minute walk from the central business district.

Conference Committee consisted of P. Bonnington, D. S. Bridges (co-chair), C. S. Calude (co-chair), M. Conder, R. W. Doran, P. Gibbons, H. Guesgen and S. Reeves (secretary). Proceedings of DMTCS'96 " Combinatorics, Complexity & Logic" was published in a new series " Discrete Mathematics and Theoretical Computer Science" by Springer-Verlag Singapore.

Scientific contribution covered a fairly large spectrum of subjects from logic and combinatorics to complexity and constructivity. The program contained 8 invited lectures, 28 contributed talks selected from 45 submissions, and 6 extra talks in two poster sessions organized by U. Guenther. Participants were mostly from New Zealand (33) but also from Australia (7), Canada (8), Finland (1), Germany (7), Italy (4), Japan (6), Netherlands (1), Russia (1), Slovakia (1) and US (4).

Conference was officially opened on Monday by Cris Calude on behalf of the organizing committee. Also W. Carson, Vice-Chancellor, R. Cooney, Dean of Science, and P. Gibbons gave a few welcome words.

The first invited speaker was R. Graham (AT & T Labs, New Jersey). In his talk he presented some old problems of the late Paul Erdös, also advertising a recently published book " The Mathematics of Paul Erdös". J. Dinitz (Univ. of Vermont) gave an interesting and graphic description of making the new MOLS table, a problem which originates from Euler's 36 officer problem. P. Odifreddi (Univ. of Toronto), also known as world's fastest recursion theorist, gave a humorous lecture of applications of simple finitistic methods in the applied sciences. Using elementary proofs, he was able to convince us that life, democracy and reality are naive or wrong or both. S. Hayashi (Kobe Univ.) introduced himself as the only representative of practical field although in Japan, the land of practicality, he is considered a theoretical mathematician. He gave an interesting talk about constructive programming. G. Rozenberg (Univ. of Leiden, Univ. of Colorado) presented a New Axiom to formal language theory. Now everything that is not (explicitly) forbidden is allowed. Languages obtained in this way are more suitable, for instance, in the very fashionable area of DNA computing. G. Chaitin (IBM New York) gave an interesting overview of algorithmic information theory, presenting his modifications to LISP which he called the set theory of computer scientist. We also learned that some mathematical facts are true for no reason, just by accident. F. Chung (Univ. of Pennsylvania) described in her talk new techniques which allow for the first time to control many graph invariants in terms of the eigenvalues and eigenfunctions. She compared the spectrum (the eigenvalues) of the graph to the spectrum of light which reveals a lot of information of distant stars to astronomers. The last invited talk was given by K. Weihrauch (Univ. of Hagen) who talked about computability in analysis, presenting Type 2 Theory of Effectivity (TTE).

The social program was abundant, starting with the reception in O'Rorke Hall where most of the participants were accommodated. Catering convinced us that all kind of slimming would fail in the forthcoming conference week. On Tuesday we took a ferry towards Devonport to have conference dinner at McHuch's of Cheltenham. The restaurant had a picturesque outlook to the volcanic island of Rangitoto. Buffet serving was outstanding, full of New Zealand specialities. During the appetizing dinner we enjoyed live classical music, and as the highlight of the evening, the great magician Bolgani performed a number of amazing card illusions.

On Wednesday the conference excursion started with a scenic drive into Waitakere ranges, about 30 km west of Auckland. Our first stop was at the Arataki Visitors Centre where, because of occasional showers, we enjoyed the beautiful surroundings in video. In Cascade Kauri Park we took a small walk to the forest to see an 800-year-old giant Kauri tree. The lunch was served in a private homestead and completed by wine tasting at Selaks Vineyards. The last visit was to the spectacular west coast beach of Muriwai, famous for its sea bird gannet colony. Though lunch had been only two hours earlier, picnic food (strawberries, cherries, grapes, cheese and crackers) served by our guide was eaten with a good appetite. Last social event was on Friday when all conference survivors were invited by P. Gibbons to a very nice party. Also in this occasion we had a chance to enjoy Bolgani's performance.

Closing ceremony took place on Friday afternoon. Organizers rewarded with a book two first-timers, Masami Ito for giving the most lectures (2) and myself for attending all the lectures. Douglas Bridges thanked Cris Calude for organizing a very nice conference. Those thanks we are all happy to join. Finally, as is the practise in ICALP meetings, G. Rozenberg told an educative story about building bridges.

DMTCS'96 was a well organized and successful conference. We are looking forward to the next meeting!