1995 Clavius Activities at Notre Dame

List of Clavius mathematiciansClavius Group at Notre Dame in 1995

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

1995 Notre Dame, Notre Dame, Indiana
Meeting #33: 25 June to 5 August

James Powell went out of his way to make us feel welcome at the University, providing us with access to the library and computer facilities as well as private offices, a large lecture room for our seminars, and a conference room which facilitated collaborative work among smaller groups of mathematicians. In addition, we were able to use DeBartolo Hall, the main classroom building on campus. Essentially all of the classrooms in DeBartolo Hall are equipped with computers and multimedia projection systems, which provided a state-of-the-art fully interactive connection to the World-Wide-Web through the campus computing facilities for several of our lectures.

Upon our arrival Dennis and Joanne Snow and the Snow family offered us a welcoming picnic supper at their home. As in previous summers at the University of Notre Dame, we resided in the O’HaraGrace Townhouses located at the east edge of the campus. As it was a particularly hot summer, we were grateful for the air conditioners which were installed by the University for each of the townhouses.

Our census for this summer meeting included 20 Clavius Mathematicians plus eight invited colleagues. Not included in this count are the faculty of Notre Dame who participated regularly in our seminars. The Clavius community, including families, grew to 49 persons. In addition, a number of guests passed through at various times during the summer.

A vital part of the Clavius Group in action at Notre Dame in 1995

Seminars

Special Topics Seminar

includes lectures on a wide variety of topics represent current research interests of the Clavius mathematicians and their colleagues.Interactive computer graphics for the geometry of surfaces
Tight polyhedral imersions of the projective plane with one handle
The Witten genus in homotopy theory
Mathematica solutions to the p/qtwist surfaces
Identification of the Dead Sea scroll fragment: a probabilistic analysis
Complex Homogeneous Manifolds
Tangent Bundle Geometry

Reflection Groups Seminar

An Introduction to Representation Theory
The Symmetric Group on Four Elements as a Coxeter Group
Representations of Direct Sums, Tensor Products, and the Dual Space
The group of isometries generated by reflection in the sides of an equilateral triangle
Representations of Symmetric Powers and Exterior Powers
Groups via Generators and Relations
Schur’s Lemma
Generalizing Finite Reflection Groups to Abstract Coxeter Groups
Representation Theory
Length Function (Humphreys, Section 5.2)
Geometric Interpretation of Coxeter Systems
Characters (Fulton & Harris, Section 2.1)
Length Functions
Characters of S_{3}
Faithfulness of the matrix representation
Representation of D_{8} and D_{12} and Q_{101}
Length in Terms of Roots

Differential Geometry Seminar

Hypersurfaces in Affine Differential Geometry
Radial and nonradial solutions of a semilinear elliptic equation
Dupin submanifolds in Lie sphere geometry
Lengths of closed geodesics in Heisenberg-like 2-step nilpotent Lie groups

Pedagogy Seminar

Taxicab geometry
Cooperative learning
History of mathematics in the classroom
Abstract algebra: using software as a teaching tool
The use of sketching in Calculus I
Teaching Advanced Calculus with Mathematica

Foliations Seminar

Introduction to mean curvature of a codimension one foliation
The Nielsen-Thurston Theory of Surface Automorphisms
Realizing functions as mean curvature of a codimension one foliation
The Kuperberg counterexamples to the Seifert conjecture
Foliations of 3-manifolds given by actions of R^2
Expansion growth of pseudogroups and foliations
Coarse cohomology for foliations
Dynamics of foliations
Isotopies of foliated 3-manifolds without holonomy
Hausdorff dimension of pseudogroups
Aubry-Mather theory in statistical mechanics

Topology Seminar

The Witten genus in homotopy theory
The Euler characteristic of a smooth manifold
An equivalent VanKampen spectral sequence
Gauge theory and symplectic manifolds