Mathematical Sciences: Number Theory and Algebraic Geometry

点击翻译按钮获取中文摘要

This research is in arithmetic algebraic geometry, the bridge area between number theory and algebraic geometry. Adolphson will continue his research on exponential sums and their associated L-functions. Wright will continue his research on the distribution of discriminants of global fields, on the basic theory of zeta functions associated to representations and on the use of his combinatorial code for the boundary of the Teichmuller space of once punctured tori in Maskit's embedding to prove Bers' conjecture on the density of cusps. Cogdell will investigate connections between zeta functions of prehomogeneous type and metaplectic forms. Yukie, the postdoctoral associate, will study geometric invariant theory, algebraic groups, and Shintani's zeta functions.