LURE Summer 2008 Research Groups

Caudill Group
The Caudill research team will focus on mathematical modeling in biology and medicine. The specific focus of the project will depend upon the interests of the team members. Some possibilities include: (1) The spread of an infectious disease through a population; (2) Models of cancer dynamics and treatment; (3) The development of antibiotic resistance in bacteria.

Davis Group
Since the early 1950s, mathematicians have worked with engineers on the question of how to efficiently transmit electronic messages through a noisy channel. For example, how should we best transmit cell phone signals?  The Davis team will consider one particular transmission scheme and will determine which binary strings will have all the desirable properties, including (i) the ease of encoding and decoding; (ii) the capability of correcting multiple errors; and (iii) the reasonable use of battery power.  We will also consider other alphabets and other applications.

Fenster Group
The Fenster research team will explore the rich and dynamic history of mathematics from 1900-1940. Student interest will drive specific research projects in diverse topics that include (but are not limited to), biographical studies of influential mathematicians, mathematics and the first world war, and developments in various mathematical disciplines such as topology, algebra and number theory.

Kerckhove Group
The Kerckhove research team will investigate how the mechanism of cell-division is related to geometric patterns that emerge from this process.  The basic idea is that since cell-division is a repeated process whose geometry is simple to describe for a single cell, perhaps the aggregate process applied many times to various configurations of neighboring cells will yield, in the long run, patterns whose  average geometry  is simple to describe. A mixture of applied (e.g. does cancerous growth effect the emerging pattern?) and theoretical (e.g. extension of investigation to higher dimensions) may be considered.

Charlesworth Group
The Charlesworth team will investigate how people solve logical puzzles like those on IQ-related tests.  The eventual goal is to create a puzzle-solving computer program (based on mathematical logic inference rules), which can also generate puzzles that are neither too easy nor too difficult for people to solve.  People who are good puzzle-solvers often begin by discovering consequences of the puzzle statement, a method called "forward-chaining" in Artificial Intelligence.  Forward-chaining is related to how research mathematicians sometimes discover new theorems (and is the reverse of how one solves typical undergraduate math homework problems).