Chair of the Department of Mathematical Sciences
Office: Business and Science Building, Room 310
Projects and Fields of Interest
- Harmonic Maps and Minimal Immersions;
- Convex Geometry;
- Middle Egyptian Grammar
- Introduction to Middle Egyptian Grammar through Ancient Writings, Linus Learning, New York, 2013 (ISBN-10: 1-60797-353-7, ISBN-13: 978-1-60797-353-9)
- Glimpses of Algebra and Geometry, Second Edition, Springer Verlag, New York, 2002 (First Edition, 1997; Japanese translation by Y. Kanie, Springer Tokyo, 2000);
- Finite Moebius Groups, Minimal Immersions of Spheres, and Moduli, Springer Verlag, New York, 2001;
- Harmonic maps and minimal immersions through representation theory, Academic Press, Boston, 1990;
- Harmonic and Minimal Maps with Applications in Geometry and Physics, Halsted Press, John Wiley & Sons, New York, 1984
Selected Research Articles
- Notes on Schneider’s stability estimates for convex sets in Minkowski space, J. of Geometry (to appear).
- Minimal simplices inscribed in a convex body, Geometriae Dedicata (June 2013) DOI 10.1007/s10711-013-9882-x.
- Simplicial slices of the space of minimal SU(2)-orbits in spheres, Contributions to Algebra and Geometry (October 2012) DOI 10.1007/s13366-012-0127-1.
- (with M. McClain) The Stela of Qema-Mar and His Household, Journal of Archaeology of the Zagreb Museum, VAMZ, 3. S., XLV (2012) 553-563. Download PDF File.
- A measure of symmetry for the moduli of spherical minimal immersions, Geometriae Dedicata 160, 1 (2012) 1-14.
- Fine structure of convex sets from asymmetric viewpoint, Contributions to Algebra and Geometry, Vol. 52, 1 (2011) 171-189.
- On the structure of convex sets with symmetries, Geometriae Dedicata, 143 (2009) 69-80.
- Convex sets with large distortion, Journal of Geometry, Vol 92 (2009) 174-192.
- Asymmetry of convex sets with isolated extreme points, Proc. Amer. Math. Soc. Vol 137, No. 1 (2009) 287-295.
- On the structure of convex sets with applications to the moduli of spherical minimal immersions, Contributions to Algebra and Geometry, Vol. 49, No. 2 (2008) 491-515.
- On the shape of the moduli of spherical minimal immersions, Trans. Amer. Math. Soc., Vol. 358, No. 6 (2006) 2425-2446.
- Spherical minimal immersions with prescribed codimension, Geometriae Dedicata, 113 (2005) 145-163.
- Critical points of the distance function on the moduli space for spherical eigenmaps and minimal immersions, Contributions to Algebra and Geometry, Vol. 45, No. 1 (2004) 305-328.
- Simplicial intersections of a convex set and moduli for spherical minimal immersions, Michigan Math. Journal, Vol.52 (2004) 341-359.
- Moduli for spherical maps and minimal immersions of homogeneous spaces, Journal of Lie Theory (2002)
- Infinitesimal rotations of isometric minimal immersions between spheres, Amer. J. Math. 122 (2000) 117-152.
- (with W. Ziller) Spherical minimal immersions of the 3-sphere, Comment. Math. Helvetici 74 (1999) 1-34.
- Universal constraints on the range of eigenmaps and spherical minimal immersions, Trans. Amer. Math. Soc. Vol. 351, No. 4 (1999) 1423-1443.
- (with H. Gauchman) Fine structure of the space of spherical minimal immersions, Trans. Amer. Math. Soc. Vol. 342, No. 6 (1996) 2551-2563.
- Eigenmaps and the space of minimal immersions between spheres, Indiana Univ. Math. J. Vol. 43, No. 4 (1994).
- Rigidity of minimal submanifolds in terms of higher fundamental forms, Michigan Math. J. Vol. 40 (1993) 493-506.
- Classification of quadratic harmonic maps of S^3 into spheres, Indiana Univ. Math. J. Vol. 36, No. 2 (1987).
- Operators on eigenmaps between spheres, Compositio Math. 88 (1993) 317-322.