Conferences

ILAS (International Linear Algebra Society)

Summer, 2006

Amsterdam, The Netherlands

WONRA (Workshop on Numerical Ranges)

Summer, 2006

Bremen, Germany

IWASEP VI (International Workshop on Accurate Solution of Eigenvalue Problems)

Spring, 2006

Pennsylvania State University

PREP (Professional Enhancement Program of MAA) workshop on Conics

Spring, 2006

Cleveland State University, Ohio

PMET (Preparing Mathematicians to Educate Teachers)

Summer, 2005

Kent State University, Ohio

ISAMA (International Symposium of Art, Mathematics, and Architecture)

Summer, 2004

Chicago, Illinois

NCTM (National Conference of Teachers of Mathematics)

Spring, 2001

Chicago, Illinois

RESEARCH

Publications

M.E. Hochstenbach, D.A. Singer, P.F. Zachlin, Eigenvalue inclusion regions from inverses of shifted matrices, June 2008. Submitted.

P. F. Zachlin, On the field of values of the inverse of a matrix, PhD Thesis, Case Western Reserve University, August 2008.

P.F. Zachlin, M.E. Hochstenbach, On the numerical range of a matrix, January 2008. English translation with comments and corrections of a 1951 paper in German by Rudolph Kippenhahn. To appear in Linear and Multilinear Algebra.

Current Work

I am interested in the boundary generating curve of the numerical range of a matrix, whether numerical range is defined in the standard way using the Euclidean inner product, or in a more general way using an inner product induced by a Hermitian matrix. In particular I am interested in relationships between the geometric properties of boundary generating curves and the algebraic properties of matrices with the associated numerical range. One other topic I am currently studying is the numerical range of the inverse of a matrix, and applications to problems in, for example, numerical linear algebra.