Number Theory Seminar: Jordan Schettler (UCSB), 'Class Numbers, Continued Fractions, and the Hilbert Modular Group'

Event Date: 

Friday, November 8, 2013 - 1:00pm to 2:00pm

Event Location: 

  • 6635 South Hall

Hirzebruch noticed "an amusing connection between continued fractions and class numbers" while computing the signature sign(X) of a Hilbert modular surface X attached to a real quadratic number field K. We will discuss how continued fractions show up in the resolution of cusp singularities in a compactification of X. The number of cusps is the class number of K, and, when K has no units of negative norm, sign(X) can be given in terms of class numbers of imaginary quadratic number fields.