1992 INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES in BURES-SUR-YVETTE, FRANCE

Clavius Group at the IHES in 1992

List of Clavius mathematicians

Hugh Albright FSC
Tom Banchoff
John Blanton
Tom Cecil
Lawrence Conlon
Margaret Freije
Richard Freije
James Heitsch
Michele Intermont
Ron Knill
John MacDonnell SJ
Joseph MacDonnell SJ
Michael May SJ
John Pouikis CSB
Sr Barbara Reynolds SDS
Patrick Ryan
Paul Schweitzer SJ
Dennis Snow
Joanne Snow
James Stasheff
William Stoeger SJ
Pedro Suarez SJ
Carlos Vasco SJ
Pawel Walczak
Andrew Whitman SJ

Clavius Community Notes

1992 INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES
in BURES-SUR-YVETTE, FRANCE
Meeting #31: 25 June to 5 August

The director of the institute Professor Marcel Berger, was attending a conference at Mount Holyoke, MA in the summer of 1991 and we made personal contact with him at that time while the Clavius group was summering at Fairfield. He encouraged us to make a formal request for our presence at the Institute for the summer of 1992. Even though there was much more demand on the Institute’s facilities than in previous summers, we were generously given for our exclusive use the two pavilions for singles and three of the larger family pavilions – 31 individual rooms and 5 doubles. The Group had to share more of the housing facilities than in the past, so we staggered the arrivals. This, however, was counterproductive because the strength of the Group has always been in achieving a maximum number of participants present at the same time. Also the high cost of both travel and living expenses forced many to remain a shorter length of time.

An important first for the group occurred regarding housing. For the first time the IHES offered the Group a grant to reduce housing expense. This was the first time that the grant went to the whole group instead of just to an individual.

A summer away from the United States is always a unique experience for the Group. The housing of the Institute also is very conducive to sharing not only among ourselves, but with the other visitors of the Institute. We realized once again that we have a unique expression of the intellectual apostolate in the Church.

Seminars

Special topics Seminar

Universal cover of proto-Haken manifolds and complements of classically wild subsets of S(3)
Exotic Cohomology
Foliations of knot complements
COBE detection of cosmic microwave background anisotropies and their interpretation
Homotopy type of some spaces of compact foliations
Traverse entropy of a flow tangent to a foliation

Differential Geometry Seminar

Introduction to affine differential geometry I, II, III
Lie curvature and Dupin submanifolds
Minkowski formulas for smooth and polyhedral surfaces

Coxeter Goups Seminar

Introduction, Examples
Root systems positive and simple roots I, II, III, IV
Presentation of the Weyl Group = Finite Reflection Group I, II, III, IV, V
Parabolic subgroups
Example dihedral group
Fundamental domains
Fundamental domains: Parabolic subgroups
Poincare polynomials of parabolic subgroups
Parabolic subgroups: Reflections in Finite Reflection Groups
Fundamental domains’ exercises
Parabolic subgroups: Lattice of parabolic subgroups
Coxeter complex