1994 Clavius Activities at the Institute for Advanced Study

List of Clavius mathematicians

Clavius Group at the IAS in 1994

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

2001 INSTITUTE FOR ADVANCED STUDY, PRINCETON, NJ

Meeting #32: 26 June to 7 August

We received a most warm welcome from the IAS on our arrival. Each person had a private office, and most had a Sun workstation in their office. We were given the exclusive use of the Mathematics Lecture Hall for our seminars, as well as the use of all of the other professional facilities of the Institute. As summer visitors of the Institute we had the privilege of living in the residences provided by the Institute in their compound. We paid the going rate for the housing but the overall cost of housing and board was reasonable and affordable to all who attended.

Our numbers this summer were 21 participating mathematicians from the Group. However not included in these counts were the many members of the Institute who regularly participated in our seminars and whom we consulted, or who consulted us during our stay. The actual Clavius Community, including the families, grew to 32 persons and in addition 29 guests.

We ran our usual Special Topics Seminar in which there were 9 presentations of various topics over a wide range of fields. The Differential Geometry Seminar was devoted to an exposition of the Holonomy Problem. Because of the absence of Vasco this summer, who was working on an educational project for the President of Colombia, the seminar in the History and Pedagogy of Mathematics had only two but profitable presentations. Finally under the leadership of May and Albright we continued with our study seminar on Coxeter Groups for a total number of 16 sessions. With respect to this latter seminar it was decided to continue next year with a different book but a related topic, the representation theory of finite groups.

The Community Life of the Group again formed one of the most important aspects of our summer gatherings. This year a good number of guests participated in our daily liturgies. Among these was the widow, Louise Morse, of the great Catholic mathematician Marston Morse, who spent a good amount of his career at the Institute. Some of her friends around the Princeton area also joined us regularly for the liturgy. The daily sermon often provided an opportunity for a more extended faith discussion, which at times carried on well beyond Mass and into the daily Social Hour.

A Clavius liturgy

Seminars

Topics seminar

7/6	Knot Polynomials	Ronald Knill
7/7	Non-existence of Locally free Actions of S1xR on Spheres	Paul Schweitzer
7/13	Relative Isoperimatric Inequalities	Thomas Banchoff
7/18	Proving Almost Spatial Homogeneity of the Universe	William Stoeger
7/19	Quaternionic Toric Spaces	Richard Scott
7/20	Introduction to Differential Geometric Invariants of Knots	Jim Stasheff
7/21	Geometry of Convex Polyhedra	Igor Rivin
7/22	Cervone’s New Tight Polyhedral Immersion	Thomas Banchoff
7/25	Uncountably many Wild Knots with the same Complement	Ronald Knill

Differential Geometry seminar

7/8	Torsion / Discrete Holonomy	Andrew Whitman
7/12	The Space of Curvature Tensors	Andrew Whitman
7/18	Dupin Hypersurfaces with Three Principal Curvatures	Thomas Cecil
7/19	Dolbeault Cohomology of Homogeneous Bundles	Dennis Snow
7/20	Isoparametric and Dupin hypersurfaces	Patrick Ryan
7/21	Coda on the Holonomy Problem	Andrew Whitman
7/22	Automorphism group of a compact complex manifold	Joanne Snow

History and Pedgogy seminar

7/14	Phase Portraits of Dynamical Systems	Joseph MacDonnell
7/22	The Arizona Calculus Software	Michael May

Coxeter Groups seminar

6/28	Review of 1993 summer
7/5	The Invariant Polynomial	Hugh Albright
7/7	The Invariant Polynomial of 12(4)	Hugh Albright
7/8	Overview of Infinite Reflection Groups	Michael May
7/11	Examples of Invariant Polynomials	Hugh Albright
7/12	Affine Reflections	John Poluikis
7/14	Calculation of the Invariants for 12(4)	John MacDonnell
7/15	The Affine Weyl Group	John Poluikis
7/18	Alcoves and Chambers – I	John Blanton
7/19	Examples of the Structure of Invariants	Hugh Albright
7/19	Examples of the Structure of Invariants	Michael May
7/21	Alcoves and Chambers – II	John Blanton
7/25	The 2-Dimensional Affine Reflection Groups	Hugh Albright
7/26	Alcoves and Chambers – III	John MacDonnell
7/28	Calculations with the Affine Reflection Group	Dennis Snow
7/29	Introduction to Representation Theory of Finite Groups	Joanne Snow