Betti Number Bounds For Varieties
and Exponential Sums
报告专家：万大庆 教授（美国加州大学欧文分校）
报告时间：9月11日（星期四）16：00-17：30
报告地点：数学学院西303报告厅
报告摘要：
We give new upper bounds for compactly supported Betti numbers of an affine variety defined by the vanishing of a system of polynomials in n variables of degree at most d. In the complete intersection case, our bound is asymptotically optimal, improving the classical bounds of Katz. As arithmetic applications, we give new total degree bounds for Zeta-functions and L-functions of varieties over finite fields, improving well known results of Bombieri, Katz, and Adolphson-Sperber.
This introductory talk is based on joint work with Dingxin Zhang.
专家简介：
万大庆，美国加州大学欧文分校（University of California, Irvine）教授，主要从事数论与算术代数几何、算法与计算复杂性的研究，涉及有限域上的Zeta-函数与L-函数，p进分析、计算数论及编码理论等方面。代表性成果发表于Annals of Mathematics、Inventiones Mathematicae，Journal of the American Mathematical Society 等数学顶尖期刊和FOCS、STOC、FOCM、IEEE IT等计算机领域顶会和顶级期刊，曾获国际华人数学家晨兴数学银奖、教育部海外杰出青年学者。
邀请人：洪绍方
