Alex Kontorovich will give the talk on Monday, March 7 at 4:15 in Math 528. This lecture will be open to all.
Abstract: A binary quadratic form is a polynomial f(x,y) = a x2 + b x y +c y2. The integers represented by a particular form are invariant under certain transformations of the form which preserve the discriminant, D = b2 - 4 a c (yes, the same one from middle school) and thus it suffices to study only the "reduced" forms. The class number h(D) counts how many reduced forms have the given discriminant, D. Gauss computed a table of the first few class numbers and conjectured his tables to be complete. The quest for an effective algorithm to answer Gauss's question runs the gamut of 20th century mathematical breakthroughs and buzzwords, from GRH and FLT to BSD and Sha. We will read this bedtime story (with no details nor proofs) until the last of us falls asleep. Oh, and there's a happy ending, of course (due to Goldfeld and Gross-Zagier).
Return to the Elementary Methods Seminar Home Page.