I.B.S. Passi

Research Summary:

The groups with the property that their integral group rings have hyperbolic unit groups were examined and some definitive results obtained (jointly with S. O. Juriaans and Dipendra Prasad).

The multiplicative Jordan decomposition property for units in integral group rings of finite groups was studied (jointly with A. W. Hales).

Augmentation powers, dimension subgroups, group homology, cyclic homology and higher traces on group rings were studied (jointly with R. Mikhailov).

Work on the book Algebra Vol.4: Field Theory, in collaboration with I. S. Luthar, was continued and completed.

Publications:

1. A contribution to Bass' conjecture [jointly with Ioannis Emmanouil], J. Group Theory (to appear).
2. Hyperbolic unit groups [jointly with S. O. Juriaans and Dipendra Prasad], Proc. Amer. Math. Soc. (to appear).
3. Augmentation powers and group homology [jointly with Roman Mikhailov],Journal of Pure and Applied Algebra (to appear).
4. Book: Algebra Vol.4: Field Theory [jointly with I. S. Luthar], Narosa Publishing House, New Delhi (to appear).
5. Book review: Subgroup Growth by Alexander Lubotzky and Dan Segal, Progress in Mathematics Vol. 212, Birkhäuser Verlag, Basel, 2003. Journal of the Indian Institute of Science (to appear).

1. A transfinite filtration of Schur multiplicator (jointly with R. Mikhailov).
2. Homology of Centralizers (jointly with R. Mikhailov).

1. International Conference on Commutative Algebra and Combinatorics, HRI, Allahabad, December 8-13, 2003.
2. The Joint India-AMS Mathematics Meeting held at Bangalore, December, 2003.
3. 91st Session of Indian Science Congress held at Chandigarh during January 2004.

Visits to other Institutes:

1. University of California, Los Angeles and San Diego (USA) (two weeks in May 2003).
2. Forschungsinstitut für Mathematik, Eidg. Tech. HocHschule, Zürich (Switzerland) (three weeks in June 2003).
3. Institut de Recherche Mathématique Avancëe, Université Louis Pasteur, Strasbourg (France) (two weeks during June/July, 2003).

1. Algebraic elements in group rings at University of California (Los Angeles), University of California (San Diego) and ETH (Zürich).
2. Jordan decomposition at Université Louis Pasteur (Strasbourg) and India-AMS special session on "The many facets of linear algebra and matrix theory", Bangalore.
3. Hyperbolic groups at the Symposium on Recent Trends in Algebra and Number Theory held at Chandigarh during the 91st Session of ISCA in January, 2004.

Other Activities:

1. Taught a course on Algebra.
2. Gave the following series of advanced lectures at HRI:
   1. Group Rings
   2. Asymptotic Group Theory.
3. Organized a weekly Seminar in Group Theory in which various visiting and local mathematicians participated.
4. Was Convener (with D. Jatkar) of the HRI Colloquium until October 2003; this is a joint programme of the Schools of Mathematics and Physics.