# International Conference on Commutative Algebra & Combinatorics

Dates: 08 December, 2003 - 13 December, 2003.

Post Conference

• Book of Abstracts
• Expository Talks :W. Bruns, Trung, S. Hosten, I. Swanson
• Book for Workshop by Rekha Thomas, Diane Maclagan and others
• Photos of conference and Workshop Information is available as attachment

On the occasion of the first International meeting of the American Mathematical Society in India organised by the Indian Academy of Sciences and Indian National Science Academy at Indian Institute of Sciences, Bangalore from December 17-21, the Bhaskaracharya Pratishthana felt it would be an ideal opportunity to further its interest in the spread of computational and combinatorial methods in commutative algebra.

The Bhaskaracharya Pratishthana appropriately has taken the lead in developing this frontier area of research in accordance with its traditions begun by its founder, and continued and extended by its present Managing committee. We have successfully organised two workshops in Computational methods in Commutative Algebra so far: The first was jointly with the University of Pune on Commutative Algebra and Invariant theory which it ran in December, 1999, and this was followed up by a workshop jointly with Harish-Chandra Research Institute, in Arithmetic and Computational Algebraic Geometry, which it ran in Harish-Chandra Research Institute, Allahabad from January 2-11, 2003. The second workshop had an international flavour with Wolfram Decker and Christoph Lossen conducting the actual computational laboratory. We are grateful to the N.B.H.M. for funding these programmes substantially, which made it possible for us to conduct them efficiently.

In view of the fact that 2003 is the 60-th year of two of India's major contributors in Commutative Algebra and Combinatorics related to it, viz. R.C. Cowsik & V. C. Dumir, we felt it would be appropriate to have a conference on Commutative Algebra and Combinatorics at this juncture. We have again approached the Harish-Chandra Research Institute, and have decided to organise an International Conference on Commutative Algebra & Combinatorics at H.R.I., Allahabad from December 8-13, 2003.

In view of the large international participation expected, it was decided to form an international organising committee which would oversee the academic aspects of the school type workshop planned in the morning sessions accessible to graduate students, and in choosing the speakers for the international conference being planned for the afternoon sessions. In the morning session the participants will be exposed to several front-line areas of commutative algebra, and some of the recent developments and open problems in those areas.

 The International Organising committee Chairman: W. Bruns, University of OsnabrÃ¼k, Member: A. Conca, University of Genoa, Italy. Member: I. Swanson, New Mexico State University, Las Cruces, USA Member: T. Hibi, Osaka University, Japan Member: R. V. Gurjar, T. I. F. R., India. Member: S. Adhikari, H.R.I., Allahabad. Member: R. Thomas, University of Washington at Seattle, U.S.A. Member: N. V. Trung, Hanoi Mathematical Institute, Vietnam. Member: S. A. Katre, University of Pune, India. Member: R. A. Rao, T. I. F. R., India.

The international committee is also entrusted with the task of finding travel funds for members from developing countries, with the help of the local organising committee. They will also assist in raising the funds required for holding the conference. This may be by approaching the national bodies like N.B.H.M., D.S.T., or other local organisations, and also via Registration fees.

 The local organising committee Chairman: R. V. Gurjar, T.I.F.R. & Managing Council, Bhaskaracharya Pratishthana. Secretary & Treasurer: S. A. Katre, University of Pune, & Managing Council, Bhaskaracharya Pratishthana. Member: S. D. Adhikari, H.R.I., Allahabad. Member: R. A. Rao, T.I.F.R. Member: J. K. Verma, I.I.T., Mumbai. Member: R. L. Karandikar, I.S.I., Delhi

The local organising committee will look after all aspects of the organisation, including raising of funds, accounts, auditing, travelling arrangements, accommodation, meals, computer facilities, and usual organisational details. We expect to invite about 30 participants from India, and about 40 participants from abroad to take part in this workshop. It will try to make arrangements for travel expenses to the Indian participants, and for all participants from either Allahabad to H.R.I. or from Varanasi to H.R.I. or from Delhi to H.R.I. (The actual purchase of tickets, and its reimbursement may be borne by us, if sufficient funds can be raised.)

Description of the Activity

The international organising committee decided to focus on a few areas of commutative algebra which were prominent today, and had open problems which could be tackled by students. It was also decided to separate the areas of research being covered in this school from those being covered in the session on Commutative Algebra being organised at the A.M.S. meet in Bangalore. We are grateful to Professor J.K. Verma, who is helping us to coordinate these aspects. Generally speaking, the more theoretical aspects of research in Commutative Algebra are being covered in the A.M.S. session on Commutative Algebra at Bangalore, whereas the present satellite conference will cover aspects of Commutative Algebra, related to Combinatorial and Computational Algebra.

Our daily schedule

The morning sessions will be of "school type" with 6 series of lectures, each consisting of 3 lectures. In the afternoon we shall have conference type talks, two of one hour (or 50 minutes) and two of 30 minutes. All the 24 speakers will be by invitation. We shall have tutorial sessions in the evenings in order to emphasize the computational aspects and to include some practical training. The following describe the series of lectures being planned.

Computational methods

1. I. Swanson: On Primary decomposition.
2. N. V. Trung: On Regularity, Local Cohomology, Reduction number.
3. Serkan Hosten: Toric Ideals: Algebra, Optimization and Statistics.

Combinatorial methods

W. Bruns: On Linear Diophantine equations leading to Anand-Gupta-Dumir Conjecture

Registration

 A Registration fee of U.S. $180 for international participants from developed countries, Rs.1000 for Indian participants, U.S.$40 plus local travel costs for members from developing countries. As per special requirements if other travel arrangements are to be made, the cost of this is to be borne by the participants. (Note: Accompanying members will also have to pay these fees.) Registration deadline: September 30, 2003. Late fee: $210. You can register here. The Registration fee will include local lodging, boarding for about 40 members. In case of accompanying members, and other restraints, the organizing committee will arrange for local lodging at an inexpensive hotel (approximately$40 per night, or \$70 for shared two members). A free bus service will be arranged from the hotel to the H.R.I. However, these members will have to bear the cost of their lodging which will not be covered in the Registration fee. They will be entitled to free breakfast/lunch/dinner at the venue of the meet daily. The decision of the organizers regarding venue where the participant will be lodged is final, but the participants can opt to choose to be lodged in a hotel outside the H.R.I. campus at his own expense, and the organizers can help him in this regards. An attempt will be made to lodge everyone inside the campus as far as possible. The Registration fee will also include the cost of transportation from Delhi-Allahabad, Varanasi-Allahabad, Allahabad-Kanpur-Agra, Allahabad-Delhi, for which the organizers will arrange for the tickets, on request of the participant. The participants will also have to bear the cost of local transportation from Delhi (or Agra) to Bangalore, but the local organizers can arrange for train tickets for these, if requested. Some participants may also want to travel to Goa, and thence to Bangalore. The local organizers can also help in arranging train tickets for this, but the participants may have to bear part of the expense from Goa to Bangalore. Members who do not wish to have any local transportation arranged for them, can have a reduced Registration fee, to be fixed by the local organizing committee. The local organizers reserve the right to reduce/waive the Registration fee in exceptional cases, for students (esp. from developing countries), and for participants who are coming for fewer days.

Second Announcement

There will be a satellite meeting of the Joint International Meeting of the A.M.S. and various Indian mathematical societies, at the Harish-Chandra Research Institute (H.R.I.), Allahabad, India. This meeting is organized jointly by the Bhaskaracharya Pratishthana, Pune and the Harish-Chandra Research, Allahabad. News about this activity will be on this site, and updated periodically.

The meet consists of three components: You are invited to indicate your interest in participating in each of these activities.

1. A series of invited lectures on current topics in Commutative algebra and Combinatorics.
The speakers include I. Swanson, R. Thomas, N. V. Trung, W. Bruns, A. Conca, T. Hibi. Speakers are requested to give a write up of about 15-30 tex pages which will be distributed to all the participants, and is likely to be published in due course.
2. A conference component in the afternoon session.
Each invited speaker will get about 30--50 minutes to give a presentation. The invited speakers are requested to send an abstract of about two to three pages, which is self-contained.
3. A (parallel) workshop on computational methods in commutative algebra for students.
The (approximately 30) sessions will be coordinated by D. Maclagan and R. Thomas in the afternoon and night sessions. Students who are doing their doctoral work, and post-doctoral students are encouraged to apply for this part.
The foreign nationals want to participate and attend the sessions 1 and 2, or sessions 1 and 3 may send the registration form at the earliest but not later than Sep. 30, 2003. They are advised to act urgently as air-tickets to India are to be purchased well in advance as December is a peak period. They are requested to send the registration fee only after their participation is confirmed by the organising committee. The seats are limited. For registration click here.

List of Participants

The following have accepted our invitation to come. They will either give three expository talks on a topic of current interest, or give an invited talk in the afternoon conference part.

Professor Aldo Conca, DIMA, Genova, Italy
Professor Marc Chardin, Institut de Mathematiques de Jussieu, France
Profesor Santiago Zarzuela, Universitat de Barcelona, Spain
Professor Hidefumi Ohsugi, Rikkyo University, Japan
Professor Kamran Divaani-Aazar, Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran
Professor Jaydeep V Chipalkatti, University of British Columbia, Canada
Professor Ming-chang Kang, National Taiwan University, Taipei, Taiwan
Professor Surinder Sehgal, The Ohio State University, U.S.A.
Professor Srikanth Iyengar, University of Missouri, U.S.A.
Professor Le Tuan Hoa, Institute of Mathematics, Hanoi, Vietnam
Professor N. V. Trung, Institute of Mathematics, Hanoi, Vietnam
Professor Nguyen Tu Cuong, Institute of Mathematics, Hanoi, Vietnam
Professor Lorenzo Robbiano, Dipartimento di Matematica, Genova, Italy
Professor Gregor Kemper, Technische Universitaet Muenchen, Germany
Professor Keiichi Watanabe, Nihon Univ., Japan
Professor Graham Leuschke, University of Kansas, Lawrence, U.S.A.
Professor Irena Swanson, New Mexico State University, U.S.A.
Professor Hibi Takayuki, Osaka University, Japan
Professor Winfried Bruns, Univeristy of Osnabruck, Germany
Professor Harm Derksen, University of Michigan, U.S.A.
Professor Rekha R. Thomas, University of Washington, U.S.A.
Professor Serkan Hosten,San Francisco State University, U.S.A. Prof. Diana Macclagan, Stanford University, U.S.A.
Dr. Clare D'Cruz, C.M.I., Chennai.

### Funding Agencies

The organizers have approached Local Funding Agencies like
• National Board for Higher Mathematics. (N.B.H.M.)
• Department of Science and Technology (D.S.T.)

International Funding Agencies
• T. S. C., International Mathematics Union (I.M.U.)

Institutions contributing towards the costs of this Conference.