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List of Clavius mathematicians## Clavius Group at Notre Dame in 1995

Hugh Albright FSC

Tom Banchoff

John Blanton

Tom Cecil

Lawrence Conlon

Margaret Freije

Richard Freije

James Heitsch

Michelle Intermont

Ron Knill

John MacDonnell SJ

Joseph MacDonnell, S.J.

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

Community

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 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.

An vital part of the Clavius Group

in action at Notre Dame in 1995

## Seminars

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

Special Topics SeminarInteractive computer graphics for the geometry of surfaces

Tight polyhedra 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 SeminarAn 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 SeminarHypersurfaces in Affine Differential Geometry

Radial and nonradial solutions of a semilinear elliptic equation

Dupin submanifolds in Lie sphere geometry

Lengths of closed geodesics in Heisenberglike 2step nilpotent Lie groups

Pedagogy SeminarTaxicab geometry

Cooperativve 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 SeminarIntroduction to mean curvature of a codimension one foliation

The NielsenThurston Theory of Surface Automorphisms

Realizing functions as mean curvature of a codimension one foliation

The Kuperberg counterexamples to the Seifert conjecture

Foliations of 3manifolds given by actions of R^2

Expansion growth of pseudogroups and foliations

Coarse cohomology for foliations

Dynamics of foliations

Isotopies of foliated 3manifolds without holonomy

Hausdorff dimension of pseudogroups

AubryMather theory in statistical mechanics

Topology SeminarThe Witten genus in homotopy theory

The Euler characteristic of a smooth manifold

An equivalent VanKampen spectral sequence

Gauge theory and symplectic manifolds

Clavius life at Notre Dame in 1995

Pertinent information about members of the Clavius Group

Clavius Activities at the Institute for Advanced Study IAS in 1989

Clavius Activities at Notre Dame University in 1990

Clavius Activities at Fairfield University in 1991

Clavius Activities at the Institut des Hautes Études Scientifique in 1992

Clavius Activities at Boston College in 1993

Clavius Activities at the Institute for Advanced Study IAS in 1994

Clavius Activities at Notre Dame University in 1995

Clavius Activities at Boston College in 1996

Clavius Activities at the Institut des Hautes Études Scientifique in 1997

Clavius Activities at Fairfield University in 1998

Clavius Activities at Holy Cross in 1999

Clavius Activities at Notre Dame in 2000

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