Number Theory Seminar
Ramin Takloo-Bighash
UIC
Rational points on one-sided compactifications of PGL(2)
Abstract: In this talk I will describe some recent results about the distribution of rational points of bounded height on
blowups of P^3. The varieties we consider can be thought of as compactificaions of the group PGL(2), and
we will use harmonic analysis on the non-commutative group PGL(2) to obtain our results. In an old work,
joint with Shalika and Tschinkel, we had studied rational points on smooth bi-equivariant compactifications
of arbitrary semi-simple groups. The varieties under consideration here are only one sided compactifications.
In concrete terms, this means that our height functions are not left and right invariant under the action of
compact subgroups of PGL(2). This introduces delicate technical difficulties that require new ideas. This is
joint work with Sho Tanimoto, and with Sho Tanimoto and Yuri Tschinkel.
Tuesday October 20, 2015 at 11:00 AM in SEO 427