Topic #1 ----------- OP-SF NET 14.4 ----------- July 15, 2007 

From: Tom Koornwinder, [email protected] 
Subject: Report on OPSFA 2007, Marseille 

Report on the 9th Conference on Orthogonal Polynomials, Special Functions and
 Applications (OPSFA9), Luminy, Marseille, France, 2-6 July 2007 

The ninth OPSFA was held during the first week of July 2007 in the nice Internat
ional Center for Mathematical Meetings (CIRM) of the French Mathematical Society
in Luminy, far out to the southeast from the centre of Marseille, at the boundary
of the large park of the Calanques (geologic formations in the form of deep 
valleys with steep sides, typically of limestone, partly submerged in the 
Mediterranean). 

Where and when have the previous OPSFA meetings been held? Curiously enough, 
there is no permanent OPSFA website giving this information, and neither is 
there an official OPSFA board, which continues in office after an OPSFA meeting.
Still, the attractiveness of the field and the closeness of informal contacts 
have been strong enough to maintain a tradition of OPSFA meetings for 23 years.


Fortunately the OPSFA9 website lists all past OPSFA conferences, but there is 
immediate confusion, since 11 meetings have preceded Marseille. However, the 
Granada and Sevilla meetings fit into a special Spanish sequence of SPOA 
meetings (see OP-SF NET 3.5 #5 for a list), and the Stieltjes meeting in Delft 
had a much wider scope. So we have the following list.


   o OPSFA1 Bar-le-Duc (France, 1984, opened by Jean Dieudonn�) 
   o OPSFA2 Segovia (Spain, 1986) o OPSFA3 Erice (Italy, 1990) 
   o VII SPOA Granada (Spain, 1991) o OPSFA4 Evian (France, 1992) 
   o Stieltjes Delft (Netherlands, 1994, in honour of Thomas Jan Stieltjes,
     1856- 1894) 
   o VIII SPOA Sevilla (Spain, 1997) 
   o OPSFA5 Patras (Greece, 1999, in honour of Theodore Chihara) 
   o OPSFA6 Rome-Ostia (Italy, 2001) 
   o OPSFA7 Copenhagen (Denmark, 2003, in honour of Richard Askey) 
   o OPSFA8 M�nchen (Germany, 2005) 
   o OPSFA9 Marseille-Luminy (France, 2007) 

Some obvious questions arise. How many of the participants in Marseille attended
all twelve listed meetings, or all nine OPSFA meetings? Probably nobody. How 
many of the participants were also in Bar-le-Duc in 1984? I would guess at least
ten.

Of course, each of these conferences emphasized certain themes, closely related
to the choice of invited speakers. It was only while writing this report that 
I found a web document describing these themes for OPSFA9 much more clearly than 
in the announcements distributed before the conference; see for instance 
OP-SF NET 13.6 #1. This web document mentions as the foremost theme 
"Orthogonal polynomials on the unit circle (OPUC) and spectral theory of 
Schr�dinger operators", writing: "Barry Simon has published in 2005 a full 
treatise in two volumes on OPUC (AMS Colloquium Publications, 54), in the 
same series where Szeg� published his pioneering book on OP in 1939. This is 
a kind of a bible on the subject, including the important recent results by 
Killip and Denissov. These OPUC are the best tool for studying discretizations 
of Schr�dinger equation and have led to very unusual results on the 
spectrum: Denissov has shown that there exist Schr�dinger operators, with 
square integrable potentials, which exhibit absolutely continuous and singular 
spectrum on the same spectral interval. It exhibits also the major theorems in 
the field (Szeg�, Rahmanov, Geronimus, Baxter, ...) including modern proofs 
and tying OPUC theory with spectral theory. This leads to deep results for 
periodic or exponentially decaying Verblunsky coefficients. This book induces 
a strong revival in the field and will be well represented at the Conference, 
since Denissov, Killip and Simon will be lecturing."

And indeed, this was really Barry Simon's conference. Not only did he give a 
plenary lecture on "Fuchsian groups and the spectral theory of finite gap 
Jacobi matrices or Peherstorfer-Sodin-Yuditskii meet Killip-Simon", but on 
earlier days he had already given two evening lectures on two "earthquakes": 

- Lubinsky earthquake: A revolution in universality and OP zeros 
(papers 199, 206 on http://www.math.gatech.edu/~lubinsky/
SelectedPapers.html ) 

- Remling earthquake: A revolution in AC spectrum 
(http://arxiv.org/abs/0706.1101 ) 

It was a good idea to have also some younger plenary lecturers such as 
Denissov and Killip, mentioned above. They both gave very good lectures, on 
continuous analogs of OP's on the unit circle, and on random OP's and random 
matrices, respectively. 

A further broad area of mutually interacting themes concerned the keywords 
Hermite-Pad� approximants, rational approximation and interpolation, 
Riemann-Hilbert problems, varying weights, multiple orthogonal polynomials, 
connections with random matrix theory, and numerical aspects (plenary speakers 
Aptekarev, Beckermann, Kuijlaars, Magnus, Stahl and Van Assche). 

The French school on Fuchsian differential equations and differential Galois 
theory, and their q-analogues, was suitably represented by Ramis.

Functional analytic aspects were covered by Lasser and Golinskii. Approximation 
theory in n-dimensional setting was presented by Plesniak. Grunbaum talked on 
matrix orthogonal polynomials, Mart�nez-Finkelshtein lectured on information 
measures of OP's, while more classical aspects of orthogonal polynomials could 
be heard in the lectures by Berg, Ismail and Marcell�n. 

Anny Cuyt reported in her lecture on the "Handbook of continued fractions for 
special functions", which will come out soon, both in book form and online; 
see already  
http://www.cfhblive.ua.ac.be/


Mourad Ismail made a short announcement of the Askey-Bateman project, a 
multi-volume series of books which will be a successor to "Higher 
Transcendental Functions" (the Bateman Project). In an evening session he 
gave interested persons a further briefing on this project. This was followed 
by a meeting of the SIAM Activity Group on OPSF, where present chair Peter 
Clarkson heard many good suggestions, about which he will probably report in 
OP-SF NET. 


On Friday afternoon Mourad headed a problem session, and Dick Askey lectured 
on problems from special functions suitable for high school teachers, in 
particular easy forms of addition formulas. These two events were additional 
to the official conference program. 

Then there were the contributed lectures, always five in parallel, so that you 
were sure to miss some that you would like to have heard. But from those that 
I could attend, and from what I read in the abstracts, I can say that there 
was a lot of good stuff. 

Social activities included an aperitif before lunch on Tuesday, and an 
excursion to the nearby charming seaside village of Cassis, from which we made 
a boat trip to the calanques, and which was followed by a conference dinner in 
a very pleasantly located restaurant. 

The organizers Galliano Valent, Jacek Gilewicz and Roland Triay, supported by 
an international scientific committee, really did a great job in making this 
conference into an important scientific event. The excellent facilities of 
CIRM (meals, lodging, library, computers, wireless network, lecture rooms) 
were very helpful in making this week a success. 

Of course, nothing is perfect, so let me list a few things which may have 
annoyed some people and from which the organizers of the next OPSFA (maybe 
in Leuven, Belgium) can learn. There were about 150 participants, which is 
more than can be accommodated by CIRM. The less privileged participants had 
to stay in student dormitories on the nearby campus, and take their meals in 
student cafeterias. Another consequence of this large number was
that the plenary lectures on the first day were held in a large lecture room 
on campus with inferior projectors. Fortunately, on the succeeding days we 
fitted without problems into the smaller, very nice CIRM auditorium. One 
draw-back of the CIRM auditorium was the difficult control of the beamer. 
Technical assistance was not always available. 

A somewhat confusing feature was the absence of a central registration area 
at the beginning of the conference. Instead, during the first days of the 
conference, one had to visit two different places in the building (a window 
and a desk) to pay or receive money. 

With the emphasis on some scientific themes, of course some others will 
receive less coverage. I missed several variables, and connections with root 
systems, groups and quantum groups. 

Some of the plenary computer presentations were really excellent, for instance 
those by Kuijlaars and by Mart�nez-Finkelshtein. But taking notes is more 
difficult with this medium. I have attended other conferences where the sheets 
of the lectures were put on the conference website. I want to recommend this 
also to OPSFA. 

The conference book is on the web, see 

http://www.cirm.univ-mrs.fr/liste_rencontre/programmes/ProgValent0727juin.pdf
Finally I suggest that the reader visit 

http://www.morewords.com/word/opsfa/