1996 Clavius Activities at Boston College

The Clavius Group at Boston College in 1996

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

1996 BOSTON COLLEGE, CHESTNUT HILL, MA
Meeting #34: 23 June to 2 August

In response to our request, Peg Dwyer (Executive Vice-President), after consultation with President Don Monan, SJ, invited the Clavius Group to spend the summer at Boston College. We were assigned to the air-conditioned Rubenstein residence hall which was the same hall we inhabited in 1993. The Assistant Housing Director, Heather Connelly, was very considerate and cooperative in allocating the resources of the residence hall. We had at our disposal four two-bedroom and ten three-bedroom apartments, each equipped with a complete kitchen, ample lounge and dining areas, two bathrooms, and a storage room.

James Woods, SJ, Director of the Boston College Summer School, arranged for classrooms in Campion Hall and in Carney. Richard Jenson, Mathematics Department Chair, arranged for carrels in the library. Both he and the Mathematics Department Secretary, Marilyn Adams, were very helpful in alerting the host department of the Clavius activities. The Mathematics Department so enjoyed having the Clavius Group around that Richard Jenson has already extended an invitation for the Group to return. Director of the computer facilities, Jeanne Spellman, was quite helpful in shortcircuiting whatever red tape might arise in access to Boston College’s extensive computer facilities. Scott Kinder, Director of the Instructional Research and Development Laboratory, and Mark Benjamin, Director of Audio Visual Support, as well as Sandy Wingaril and others in the Boston College administration were also very helpful.

At the peak of our summer gathering, we occupied fourteen of these apartments: four of these were used by the male religious community (nine Jesuits, a Christian Brother, a Basilian Father, along with three lay men), one by the women (a Salvatorian Sister and two lay women), and nine by the families. Our census for this summer meeting included 24 Clavius Mathematicians plus 8 invited colleagues. Not included in this count are the faculty of Boston College who Participated regularly in our seminars. Guests came through at various times during the summer, some staying for only an afternoon, others staying for several weeks.

An important part of the Clavius schedule at Boston College in 1996

Seminars

Special Topics Seminar

These lectures on a wide variety of topics represent current research interests of the Clavius mathematicians and their colleagues.

An Introduction to Model Theory
Freedom of Expression and the Internet
Nuetrinos
Laguerre Geometry and Conic Sections
Explorations in Euclidean and Taxicab Metrics
Building Cellular Approximations of Spaces
The Director Circle
Limits on Cosmological Anisotropies and Inhomogeneities

Representation Theory Seminar

In this working seminar, participants worked in selected portions
of the text: “Representation Theory” by Fulton & Harris.

Introduction to Character Tables of Symmetric Groups
Some Examples of Young Diagrams for S-5
An Introduction to Character Tables
Deriving the Hook Length Formula from Frobenius Formula
Characters of Exterior Algebra Representations of Symmetric Groups
The “Rim Hook” Method for Calculating Character Tables
Character Table for S-6 Calculated from the Frobenius Formula
Orthogonality of Characters of Finite Groups
Addition and Multiplication of Characters of Finite Groups
The Alternating Group, A-5
The Subgroup of Rotations in D-8
An Induced Representation of D-8 Using the Subgroup of Rotations
The Character Table for S-4
Exterior Algebra: An Example Involving S-4
The Interior Product: An Example Involving S-4
Character Table for S-4

Differential Geometry Seminar

Shape Operators of Real Hypersurfaces in Complex Space Forms:I II III IV
Tight Immersions of Highly Connected Manifolds, part 1 & 2
Dupin Submanifolds in Lie Sphere Geometry, part 1 & 2
Affine Translation Surfaces in R^4
Curvature of Homogeneous Vector Bundles, part 1 & 2

Pedagogy Seminar

In this seminar, we discuss our experiences in our classroom teaching.

Cooperative Learning in a Computer Lab with ISETL
Teaching Group Theory with Computer Packages
The Nuts & Bolts — What works? What doesn’t? — A discussion
Interactive Illustration for Teaching and Learning Differential Equations
A Converging Sequence of Hyperpowers
The Concept of Function in Calculus and Algebra
A First Proof Course: The Nuts & Bolts — A Discussion
Paperless Classroom and Geometry on the Internet

Topology Seminar

Riemann Manifolds not Quasi-isometric to Leaves
Classifications of Depth One Foliations
Vanishing Cycles and Generalized Reeb Components
Torsion for Foliations