Manin's conjecture and balanced line bundles
Sho Tanimoto, NYU

Manin's program, initiated by Y. Manin and others and significantly developed over the last 20 years, relates the asymptotic distribution of rational points of bounded height on algebraic varieties $X$ to global geometric invariants of $X$. In this talk I will discuss our recent development of theory of height zeta functions which is joint work with Y. Tschinkel, then discuss some geometric issues arising from Manin's conjecture. The later research is joint work with B. Hassett and Y. Tschinkel.