Presentation :

General Overview,

           The ICMPA became the UNESCO Chair of Mathematical Physics and Applications in April 2005, following the application introduced by its Holder, Professor Mahouton Norbert Hounkonnou, via the proper administrative hierarchical procedure (the University of Abomey Calavi, the UNESCO National Commission, the Benin Permanent Delegation at UNESCO), following an earlier application in November 2004 within that framework introduced by Profs. Jan Govaerts (Belgium), M. Norbert Hounkonnou (UAC) and Alfred Msezane (USA). Such a mark of distinction of the ICMPA by UNESCO results from the quality of the activities led by the Chair since its creation in 2001, as well as from its partnership with UNESCO since 2002.
Indeed, the ICMPA is a dynamic network working through active coordination of selected partners in various regions in Africa as well as in European and North American scientific institutions. The activities of the ICMPA involve the following partners.

i) from African Universities: University of Lome, Togo (Coordinators: Professor Komi Tchakpele and Professor Koffi Assiamoua), University of Zambia, Zambia (Coordinator: Dr. Habatwa Mweene), University of Lesotho, Lesotho (Coordinator: Dr N. P. Rapapa), Ecole Normale Supérieure, Cameroon (Coordinator: Professor Mama Foupouagnigni), University of Yaounde 1, Cameroon (Coordinator: Professor Paul Woafo and Professor N. Noutchéguémè), University of Ibadan, Nigeria (Coordinator: Dr U. N. Bassey), University of Ouagadougou,Burkina-Faso (Coordinator: Professor Blaise Some), University Marien N’gouabi, Congo-Brazzaville (Coordinator: Professor Bernard M’Passi-Mabiala), University of Kinshasa, Democratic Republic of Congo (Coordinator: Professor O. R. Walo), University Moulay Ismail, Meknès, Morocco (Professor Abdelkader Makhoute), Faculty of Sciences Dhar Mehraz, Morocco (Coordinator: Professor F. Lahlou), University of Sciences and Techniques of Masuku, Gabon (Coordinator: P. Nang), etc.

ii) as well as from outstanding European and North American scientific institutions like the Catholic University of Louvain, Louvain-la-Neuve, Belgium (Coordinators: Professor Jan Govaerts and Professor Jean-Pierre Antoine), Clark Atlanta University, USA (Coordinators: Professor Alfred A. Z. Msezane (Clark Atlanta University), Professor Gerard A. Goldin (Rutgers University), Professor William A. Lester, Jr. (University of California at Berkeley) and Professor James Gates (Maryland University), Concordia University, Canada (Coordinator: Professor Twareque Ali), Paris-Sud XI University, France (Coordinators: Professor Xavier Chapuisat and Professor Vincent Rivasseau), University of Perpignan, France (Coordinator: Dr Georges Debiais), Paris 7 University, France (Coordinator: Professor Jean-Pierre Gazeau), University of Bialystok, Poland (Professor Anatol O. Odziejewicz), Ecole Polytechnique Fédérale de Lauzanne, Switzerland (Professor Tudor Ratiu), etc.

The ICMPA benefits from professorships of the Abdus Salam International Centre for Theoretical Physics (ICTP, Trieste, Italy). Professor J. Govaerts from the Catholic University of Louvain (Belgium) and Professor T. S. Ali from Concordia University (Canada) hold now such positions at ICMPA and are fully involved in the PhD and Master degree programmes. Following the selection of the ICMPA project as of first priority for the UNESCO International Basic Science Programme, ICMPA currently has been managing the implementation of the UNESCO/IBSP project 5-BJ-01 Development of mathematical physics in Africa: Organization of international workshops on contemporary problems in mathematical physics (COPROMAPH)  of COPROMAPH international schools since 2005.  In the framework of the ICMPA international MSc programme in geoinformatics for water and ecosystem management and doctoral  programme in water and environment sciences, ICMPA started a collaboration with the International Institute for Geoinformation Science and Earth Observaton (ITC) in Enschede, the Netherlands. This initiative was in response to a specific request from UNESCO in the framework of the GOOS-Africa Programme and the UNESCO Crosscutting Project on the Application of Remote Sensing for Integrated Management of Ecosystem and Water Resources in Africa, for which ICMPA has been selected as participating institution. In this platform, it was agreed to pursue collaboration, starting with software support and guest lectures, in preparation for exploring the possibilities for funding collaboration in order to further strengthen the MSc and PhD programmes.  The Bonn Chuvenky University, Germany (Coordinator: Dr H. P. Thamm)  and the LTHE, Grenoble, France (Coordinator: Th. Lebel) are also involved in these programmes. Our Chair is also actively involved in the African Monsoon Multidisciplinary Analyses (AMMA) programme.
Furthermore, ICMPA has signed collaboration agreements with local governmental enterprises working in the fields of the above MSc programmes, namely with the Benin Agency for Environment (ABE) and the National Centre of Remote Sensing and Forestry Observation (CENATEL).
For the sake of convenience, let us briefly recall the ICMPA objectives and relevant activities. The International Chair in Mathematical Physics and Applications (ICMPA) grew out of the International Workshops on Contemporary Problems in Mathematical Physics (COPROMAPH International Workshops) that the Republic of Benin has been organizing every two years since 1999 and which constitute outstanding scientific meetings of international standard. Its creation has been sealed by the Departmental Order n° 024/MESRS/CAB/DC/SGM/SP dated April 19th, 2002, taken by the Benin Minister in charge of Higher Education and Scientific Research. 
One of the main objectives of the COPROMAPH International Workshops is to contribute to the development of a critical mass of researchers in Africa in as dynamic an area as is mathematical physics. The Workshop brings together specialists in Theoretical and Mathematical Physics.  It offers the international scientific community an arena for interactions  and presentations of scientific research results on contemporary problems in these fields. The Workshop also provides young African researchers an opportunity to know each other and  initiate scientific collaboration. Hence, the Workshop contributes in strengthening the  research capacity and revitalizing activities in mathematical physics in African universities.
The first edition of the COPROMAPH International Workshops (COPROMAPH1) took place in Benin in November 1999 and has been effectively attended by 103 researchers coming  from USA, Canada, Belgium, France, Morocco Kingdom, Senegal, Burkina-Faso, Congo  Burundi, Cameroon, Ivory Cost, Gabon, Chad, Niger, Democratic Republic of Congo,  Togo and Benin. Twenty-one (21) plenary lectures and thirty-six (36) communications have been presented.
The second edition (COPROMAPH2 International Workshop) also took place in Benin as planned, from October 28th  to November 2nd, 2001 with at least as much success as the first edition. Researchers from other countries such as Lesotho, Zambia, Poland,  Switzerland joined the list of the participants.
The COPROMAPH3 International Workshop has been organized from November 1st to November 7th, 2003 with 155 participants. This up-trend in participation also translates into the definite improvement in the quality and variety of contributions and the increase in the number of contributed papers from one edition to the next. At COPROMAPH3 there have been 37 plenary talks and 71 brief communications. Following a stringent refereeing procedure, these contributions are also included in a series of Proceedings Volumes published through World Scientific Publishing, which prove to be of great value as references texts for African scientists (and have grown from some 380 pages long for COPROMAPH1 to 630 pages for COPROMAPH3). These statistics prove that the COPROMAPH International Workshops attract an ever increasing great interest from African researchers. Thus, the ICMPA is today at the core of a major dynamic and active network of specialists in the fields of Theoretical and Mathematical Physics within Africa. A standing which was confirmed once again by the success of the Fourth Edition of the COPROMAPH Workshops, having taken place in Benin from November 5 to 11, 2005. On that occasion and given the International Year of Physics 2005, the First COPROMAPH International School was also launched with a week of graduate level lectures and tutorials, and participating student seminars, during the week preceding the actual Workshop, and in preparation for it (see further below).
Indeed, the most significant action undertaken at the COPROMAPH2 International Workshop in November 2001 is the creation within the University of Abomey-Calavi of an International Chair in Mathematical Physics and Applications, namely ICMPA in brief. The birth of this Chair is justified by the necessity for Africa not to stay out of the development of Mathematical Physics in the World. The purpose is to create a permanent framework for exchange of research results as well as to stimulate the young generation of mathematical physicists to bring a contribution of quality in their field.
       The founding members of the ICMPA come from 12 African Universities, 4 North-American Universities and 5 European Universities. They have defined the objectives of the Chair as follows:

i) To work out and spread the knowledge and the know-how in Mathematical Physics and Applications;

ii) To promote young people and women in the area of Mathematical Physics and Applications;

iii) To look for active partnership between the Chair and other companies and industries for concrete applications of Mathematical Physics to problems of development.

Those objectives, in the considered field, go through:
- Boosting research;
- Periodic reports on the main results;
- The promotion of the young researchers;
- Researcher periodical meetings in order to exchange experiences and to break the isolation of young African researchers.

The ICMPA activities derive from the preceded objectives and mainly include:
- The organization every two years of the COPROMAPH International Workshop;
- The organization every year of  an International School;
- The allocation of excellency scholarships;
- The defence of excellency thesis to the credit of the Chair during COPROMAPH  International Workshop;
- The development and distribution of annual scientific reports on the publications and other research activities of the Chair's members;
- Joint supervision of doctorate theses;
- Exchanges of visiting professors, researchers and PhD students;
- Housing for researchers and students undertaking research in centers and research institutions affiliated to the Chair.

The COPROMAPH International Schools are intended for the young researchers and PhD  students of African universities, and aim at providing basic self-contained lectures and tutorials on topics of interest, developed in one-two weeks by a renown expert. Selected participants at these schools receive a Certificate of participation.

The ICMPA is run by an Executive Secretariat elected, then appointed by the Departmental Order n° 2003/052/MESRS/CAB/DC/SG/R-UAC dated July 29th, 2003. The setting-up of the management of the young Chair as well as the conditions which presided to its birth are a guarantee of its international character and a solid asset to its ability to converge all possible and useful expertises to achieve its objectives. Concerning the training program, the ICMPA has created for the best students coming mainly from African universities:

i) a PhD program in Mathematical Physics,

ii) a PhD program in Water and Environment Sciences, and

iii) a vocational training program of Professional Master type in the fields related to the development practical matters such as Remote Sensing and its applications to the Integrated Management of Water Resources and Ecosystems.

These last  two training programs have been introduced following the UNESCO-Africa Project on Network Application  of Remote Sensing for Integrated Management of Ecosystems and Water Resources for which the  young Chair has been selected in 2002. To launch  these programs, the Chair received from UNESCO a financial support of 13,125 EUR  on the basis of an Activity-Financing Contract co-signed in July 18th, 2003 by the Director of Higher Education Professor K. SEDDOH, on behalf of the Director General of UNESCO, and  the President of ICMPA, Professor M. N. Hounkonnou. The Benin Government has provided the Chair with the staff salaries, the necessary structures and installations for its functioning. Still for these last two training programs - Water and Environment Sciences and Remote Sensing and its applications to the Integrated Management of Water Resources and Ecosystems - the Chair has signed a partnership agreement with national research centres and production units involved in these applied fields such as the National Center for Remote Sensing and Forestry Supervision (Centre National de Télédétection et de la Surveillance du Couvert Forestier) and the Benin  Agency for the Environment  (Agence Béninoise pour l'Environnement) to profit of their expertise, infrastructure and equipments.
The ICMPA also receives young African researchers and PhD for one-or two - year postdoctoral or short research stays. During their stay at the Chair, the fellows also intend to assist the University's Departments and the Institut de Mathématiques et de Sciences Physiques of Porto-Novo in teaching and research activities.
The ICMPA also assists the best undergraduate students with limited
resources of the Université d'Abomey-Calavi, by  giving them grants.

The fourth Workshop (COPROMAPH4) was organized as a satellite conference to the IUPAP World Conference on Physics for Sustainable Development (WCPSD) held in Durban, South Africa, October 31st to November 2nd, 2005, on the occasion of the World Year of  Physics 2005. The Workshop has included a thematic lecture series, invited review talks and contributed communications. The invited review talks have been presented in plenary sessions whereas the specialized contributed papers have been  presented in appropriate parallel working groups. To also celebrate the World Year of Physics 2005, a new event was launched in parallel to the Workshop, namely the COPROMAPH International School which has preceded the COPROMAPH International Workshop. The aim of this School was to provide basic self-contained set of lecture series and tutorials for PhD students and younger COPROMAPH Workshop participants, on topics of interest in anticipation of the more advanced presentations at the Workshop. Student seminars were also organized.
The dates were:

i) COPROMAPH International School:
o Superstrings before the 1995 revolution
o Quantum mechanics and fields for physicists and  athematicians  
            Monday, October 31st - Friday, November 4th, 2005;

ii) COPROMAPH4 International Workshop:
o Superstrings after the 1995 revolution: M-Theory 
       Saturday, November 5th - Friday, November 11th, 2005.

The series of COPROMAPH Workshops  is thus one of the main activities of the International Chair in Mathematical Physics and Applications (ICMPA) which, as far as we know, is the major network within Africa bringing together experts in Theoretical and Mathematical Physics coming from at least 12 African Universities,  4 North-American Universities and 5 European Universities. The number of participants  in the COPROMAPH International Workshop has seen a steady increase from one edition to the next, especially of the younger African researchers finding there also a unique opportunity for presenting their work and engaging in scientific exchanges and collaborations.

           The originality of the COPROMAPH International Workshop consists in the fact that among all the presentations, two general topics are chosen to be discussed on continuous basis throughout the week as a series of self-contained lectures on a specific topic. The  detailed set of notes of these lectures are asked to be available a month or so before the workshop, to enable all participants to benefit best from oral presentations. For such a series of lectures, the space foreseen in the Workshop Proceedings is some 80 pages or so.
            Building on the success of its first edition, held in 2005, the objective of the second edition of the COPROMAPH International School was to bring to attending students and other researchers an in-depth familiarity with some current mathematical and physical problems in the area of quantization techniques. Such techniques form an active area of                  research in present day mathematical physics, in so far as they are at the basis of much work in particle physics, representation theory   and symplectic geometry. The other objective was to familiarize the audience with the existing literature in the subject and its related domains. Finally, the School attempted to promote dialogue and interaction among the participants, with the expectation that research collaborations would develop between researchers from different countries. The longer term objective is to contribute to the development                       of a critical mass of researchers in Africa in the dynamic area of mathematical physics. The School also gave young African researchers an opportunity to know each other and initiate scientific collaboration, contributing to the strengthening of the research capacity and to revitalizing activities in mathematical physics in African universities.
This  Second Edition of COPROMAPH International School was held in Benin, from December 11th to December 16th, 2006 on the theme: Quantization Techniques: Mathematical and Physical Aspects
The third International COPROMAPH School, held from October, Monday
22 to Friday 26, 2007. Two separate lectures series for two courses, one on a “Pedestrian Introduction to Quantum Physics’, and the other on ”Quantisation and Geometry”, were delivered for 1.5 hours every morning for each course by Professor Jan Govaerts from catholic University of Louvain (Belgium), hence a total of 15 hours of lectures during that week. The chosen topics were in anticipation of the general theme, “Noncommutative Geometry and Gauge Theories”, of the COPROMAPH5 Conference that started on Saturday, October 27, 2007, in order also to prepare the younger scientists attending the Conference to benefit the most from it in spite of the high scientific caliber of the Conference. The some 40 participants to the COPROMAPH School also had the opportunity to spend each of four afternoons (the whole week except for Wednesday afternoon) about 1.5 hours in tutorial sessions related to the lectures of the morning.
Both the courses and tutorials relied on written material, in the form of course notes and tutorial problems including even their detailed solutions. The 40 participants originated not only from Benin itself, but also quite a many of the neighbouring countries
(Niger, Nigeria, Burkina Faso, Togo, Ivory Coast) but also from further afield (Cameroon, Senegal, Lesotho, Zambia, ...). In spite of their varied scientific backgrounds, a greatest deal of them expressed on many occasions their appreciation of the courses and tutorials, and the scientific knowledge laid out to them throughout the week. Furthermore, on each of four afternoons (except for theWednesday afternoon), short seminars (20 minutes) by participants were organised, so as to open the discussion among them, expose them to what their colleagues from elsewhere in Africa are doing in terms of research, and providing thus also a somewhat informal area in which to acquire experience of public presentations in front of a critical audience. These seminars also offer a unique opportunity to realise that English is presently the language of science, and French speaking African participants quickly adapted to having to communicate in that other language. 
Such a School, as well as the COPROMAPH Conferences, offers a unique opportunity for these young African scientists to foster new scientific contacts and lines of communication within the African continent, a very crucial factor for its future development.  During the week of the COPROMAPH School, a general public conference was organised and widely announced in the local media, also with the official support of the Minister for Research, Higher Education and Technology. It took place on Wednesday afternoon, October 24, 2007. High school pupils from all schools in Cotonou were especially invited, and large numbers attended together with their mathematics and science teachers. The theme of the conference was “L’Univers au coeur de l’atome” (The Universe at the center of the atom), and it was a great success indeed. The large auditorium was overflowing, and some people had (unfortunately) to be turned away by lack of space. TV and radio were there for interviews afterwards and even came back the days after the conference, and provided some of the news on local media outlets. Being away on an urgent business, the Minister sent her Director of Cabinet to officially open the conference. And the large and varied collection of many questions afterwards proved the great interest and curiosity the conference raised. Following the conference large numbers of young people wished to have pictures taken and signatures given with me, and spontaneously asked with a great deal of impatience, in particular young ladies having a calling for science, a unique circumstance which calls for future efforts, “When is the next conference taking place?”. This general public conference has had a great impact indeed, and was especially targeting the younger generation of high school students. It followed a similar one in November 2005 on the occasion of the World Year of Physics 2005, already a success then, and is called to become quickly a tradition in Cotonou whenever possible, and certainly on the occasion of any future COPROMAPH School and Conference. Support towards high school students and their mathematics and science teachers has also become one of the objectives that the CIPMA-UNESCO has set itself for its future action in the country of Benin. On the inauguration evening of the Conference itself, in an impromptu speech I had to give before the Minister herself, precisely that suggestion was made explicitly among some others. The Minister was particularly moved and improvised beyond her written speech that this very topic is very dear and close to her preoccupations, and that she would call on the CIPMA-UNESCO and Professor Govaerts for initiatives and actions into such a direction as well. If such ideal is to become concrete reality in the foreseeable future, such general public conferences, of which the tradition was launched on Professor Govaerts first visit under the auspices of the ICTP programme in November 2005 again on the occasion of the World Year of Physics 2005, will have had indeed a lasting impact on the scientific scene in Benin.
Once again, the COPROMAPH5 Workshop was attended by over 100 participants from different African countries from all over the continent, as well as some colleagues from Europe and North America. In particular, a young mathematician, colleague of mine at the Catholic University of Louvain, Professor Pierre Bieliavsky, had accepted to come deliver a series of lectures on noncom- mutative geometry. Not only were these lectures a great success and they met with the participants’ huge interest and appreciation, but also with Pierre Bieliavsky has the CIPMA- UNESCO Chair, COPROMAPH, and Benin found a new true and genuine friend. As usual, besides the course running every morning for seven days throughout the Conference, other colleagues, whether from out-of-Africa or more importantly from the African continent, also presented high-level plenary talks, while most participants presented their own research in parallel sessions organised each afternoon of the seven days Conference, except forWednesday, October 31st, 2007.
On October 31st, 2007, three PhD students, having all three benefited from the ICTP PhD Fellowship Programme granted to the CIPMA-UNESCO over the last three years, (Joseph Ben Geloun (from Senegal), Mahaman Kabir Mahaman (from Niger) and Aderibigbe Anjorin (from Nigeria), also defended their PhD work in front of the COPROMAPH5 participants.
The repeated success of the bi-annual COPROMAPH Workshops, henceforth to be accompanied by the annual COPROMAPH Schools, is proof that these events are meeting the great needs of the African scientists active in mathematical and theoretical physics, and even physics in a wider sense. Being de facto also the editor in charge of the Proceedings of theseWorkshops (published since 1999 by World Scientific, Singapore), over the years I have witnessed a steady increase in the quality, not only of the oral presentations but also of the submitted contributions to the Proceedings, especially those by the younger African scientists. After all, most of these efforts find their primary motivation in seeing the present young generation of African scientists grow quickly into mature contributors to research of the highest international standards. So far, all the efforts invested in the COPROMAPH Workshops, and likewise through the ICMPA-UNESCO Chair, have proved to give very promising impetus into such a direction. These efforts deserve only to be supported further, and more vigorously certainly, and under a scope as large as feasible. The ICTP, through its present support for PhD students and Postdoctoral positions at the ICMPA-UNESCO, and likewise to all past COPROMAPH Workshops but for the very last, which is hoped to be a single exception, has been instrumental in this success. In order to see the due fruition of all this investment, it is crucial that the ICTP may continue, and even increase, this support, foremost to the benefit of the younger African scientists who have now found through the COPROMAPH Workshops and the ICMPA-UNESCO the means for a steady progress and growth in science on the African continent.

The accounts of the International Chair in Mathematical Physics and Applications are maintained in accordance with the principles of “fund accounting”. This is the procedure by which resources for various purposes are classified for accounting and reporting purposes into funds that are in accordance with activities or objectives specified. Separate accounts are maintained for each fund; however, funds that have similar characteristics have been combined into the same account. For the year 2003 for instance, apart from the COPROMAPH Workshop that has been funded by a group of sponsors (ICTP; the Catholic University of Louvain, Belgium; the International Association of Mathematical Physics, University of Paris Sud XI, Institut de Recherche pour le Développement (France); Belgian University Cooperation CUD-CIUF, University of Abomey-Calavi (Benin), Centre Béninois de la Recherche Scientifique, the Benin Government, etc.), the training programs have been supported  by  UNESCO;  the personnel salaries and the current functioning are supported by Benin government.

The ICMPA 2007 research activities deals with the deepness of the topics started these three last years, namely the  investigations on {\it Nonlinear Models and Symmetries   in Mathematical Physics}, which include the following main parts:
 

¨ Symmetries of Heun's operators, factorization and basic sets of Chebychev polynomials

¨ Nonlinear models in noncommutative geometry  This work deals with two main aspects of nonlinear models:

§ Nonlinear solvable models: deformed spin-orbit and Landau operators;
§ Symmetries and nonlocal aspects of noncommutative field theory (a nonperturbative study)

¨ Symmetry analysis of nonlinear hydro-biological models;

¨ Nonlinear deformed systems and generalized quantum polynomials.