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 4dimensional diagrams. Each of these sets of diagrams represented a point in a space of 4dimensional, 5pointed simplexes that exist in the 4dimensional 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!
Biomathematics
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.
