Student colloquium

"The tale of a little point on a sphere that factored a large integer"

This is a tale about the brave warriors, who called themselves ”Ipotds”, or ”Integer points on a three-dimensional sphere”. Ipotds lived happily on the sphere, their lives were filled with joy and laughter, until the giant by the name of Soros, the ”Square of a radius of a sphere”, came to their little planet and stole the sun. For a long time, brave ipotds didn’t know how to drive the giant away, until a diviner told them that Soros had only one weak spot - it was an integer, and the only way for it to return the sunlight was to divide it evenly by some non-trivial factor.

Soon, the wise men of ipotds who lived in the library found the manuscripts of Gauss, Hurwitz and Venkov, who developed a theory which connected their people to class groups of imaginary number fields with the help of the brave warriors from a tribe that lived overseas, the ”quaternions”. When quaternions came to rescue, the great battle with Soros began. On Friday 23rd, we shall witness this battle, and by looking at the class group of imaginary quadratic fields through the perspective of quaternions, we will see how one brave little point on a three-dimensional sphere slayed the giant Soros, and factored the integer.