I grew up in Dayton, Ohio and attended Catholic elementary school, high school, and college. I have always liked mathematics and was completely hooked when I was shown a one-sided Mobius strip in the second grade. After graduating from the University of Dayton, I went to Ann Arbor, Michigan to earn a Ph.D. in mathematics from the University of Michigan (although I remained a Buckeye fan). After a postdoctoral appointment at the University of Oklahoma (still a Buckeye fan), I moved to Erie to join the Mathematics Department at Gannon.
I am married and have four children. My wife also graduated from the University of Dayton and earned a Ph.D. in organic chemistry from the University of Michigan. She has now chosen to devote her life to a full-time career raising and home-schooling our children.
My research interests lie in the field of commutative algebra, specifically tight closure theory, characteristic p methods, and big Cohen-Macaulay algebras and modules.
I study generalized number systems (called “rings”) that behave like the integers or real numbers in many ways but can also behave quite differently. Such systems arise when one studies solutions to systems of equations. I am particularly interested in rings where a fixed number (usually prime) is set equal to 0. (Imagine how 24 = 0 in a 24-hour clock.) Rings also possess geometric information, just as the solutions to y=x^2 can be thought of as a parabola in the plane. Moving back and forth between the algebra and geometry involved can often help one understand both areas better.
I have recently become interested in the history of how algebra has been taught in high school in the United States.