Matt Boelkins

My research interests are broadly in analysis and numerical analysis, largely focused on the relationship between the sets of zeros and critical numbers of polynomials.  

Much of my recent work has been centered on real polynomials with all real, distinct zeros (PwDRZ).  A key class of such functions is families of orthogonal polynomials.  Several recent papers have uncovered many interesting properties of PwDRZs.  The java applet in the left below above helps demonstrate Bruce Anderson's Root Dragging Theorem (click and drag on one of the red boxes), while the image on the lower right is of a PIPCIR -- a Polynomial whose Inflection Points Correspond with its Interior Roots -- an extremely interesting class of polynomials discovered by Anderson in 1997.   

I am also interested several problems related to the Sendov Conjecture and polynomials whose zeros all like in the complex unit disk.

More about my research interests and work with undergraduates can be read here.  This coming summer I will be a faculty mentor in the 2008 GVSU REU.

I also really enjoy mathematical history; one of my favorite topics is the Basel Problem, solved by Euler and beautifully discussed in Bill Dunham's marvelous book.  The follow-up question on the sum of the reciprocals of the cubes is of interest, too, and still open.  All that's really known is that the sum of the reciprocals of the cubes is irrational.