Co-Lab Seminar

Searching for rational solutions to polynomial equations

Speaker: Anand Deopurkar (MSI)

Searching for rational solutions to polynomial equations.

Many interesting problems in mathematics involve solving a system of polynomial equations where the solutions are rational numbers (see the next talk, for example). Given a system of equations, can we determine if a rational solution exists? Can we tell how many solutions there are? Can we enumerate them all? I will discuss computational and geometric aspects of these questions.

Searching for perfect triangles

Speaker: Ralph Buchholz (DST)
A perfect triangle is a one with rational sides, medians, and area. It is unknown whether such a beast exists or not! It turns out that searching for a perfect triangle is equivalent to searching for a rational solution of a system of polynomial equations. This problem is thus a perfect arena to explore the computational and geometric aspects discussed in the previous talk. I will describe the objects we encounter in this quest and what they tell us about the original question.

This event is free and open to the public. It will be followed by drinks and nibbles on Level 3 of the Hanna Neumann Building (145).

The Co-Lab Seminar Series is supported by the Mathematical Sciences Institute at the College of Science, the Research School of Computer Science at the College of Engineering & Computer Science and the Co-Lab at the ANU.