We will present some (hopefully) interesting results in probabililty theory.

We will discuss the quantum Fourier transform for an arbitrary
finite abelian group, and Hallgren's adaptation of Shor's algorithm to
uncountable abelian groups—namely, to $\mathbb{R}$. Both pieces are
essential ingredients in the quantum algorithm of
Eisentr\"ager-Hallgren-Kitaev-Song to compute the unit group of a number
field. Suggested readings are Hallgren's Pell equation paper and Jozsa's
exposition on the quantum Fourier transform; as usual, both are
available at

http://public.csusm.edu/ssharif/crypto