Waves Tetrahedrons Biomathematics Root Systems

Summer Research Experience 2004

Nine students. Eight professors. Six research topics. Three months. One website. The best and brightest undergraduates of UMass' math department work on various topics in pure and applied mathematics.

Shockwaves and Rarefractions

Pictures, movies and programs; under the supervision of Robin Young, Robert Chase and Patrick Dragon examine shockwaves arising from partial differential equations. Associated with systems of PDEs is a flux matrix whose eigensystem suggests wavelike phenomena. In addition to their main results, they give a chronology of their work that might be helpful for undergraduates studying hyperbolic systems of PDEs.

The Topological Space of Tetrahedrons

Under the supervision of Paul Gunnells, Daniel Epstein created a lengthy succession of Java programs to manipulate the colorations of the edges of sets of 2- through 4-dimensional diagrams. Each of these sets of diagrams represented a point in a space of 4-dimensional, 5-pointed simplexes that exist in the 4-dimensional complex projective space. By coloring the edges of a given set of diagrams, he was collapsing its corresponding simplex into a degenerate form. Sound intriguing? Check it out!


Under the supervision of Nate Whittaker, Marc Maier, Heather Harrington and Lesantha Naidoo model angiogenesis and the growth of cancer cells. Power Point presentations guide the viewer through this exciting and important work. From a single dimension to the surface of the eye, this team explores various simulations. Multiple species interact in probabalistic ways.

Characteristic Numbers in Field Theory

Under the supervison of Farshid Hajir, Mike Higgins studies the charactaristic numbers of fields.

Root Systems

Under the supervision of Ivan Mircovich, Ross Murray constructs the Anderson polygons and examines their equivalence classes. Start with a root system, a set of vectors along with hyperplanes perpendicular to them. Consider the group of isometries that arises from reflections across the planes. This is the Weyl group. His study goes on from there.

Ordinary Differential Equations

Under the supervision of Floyd Williams, Jooyoung Kim explores ordinary differential equations. Her work relates to quantum mechanics.


Produced and maintained by Robert Chase, the Department of Mathematics and Statistics