数学大讲堂

Applications of Linear Algebraic Methods in Combinatorics and Finite Geometry

嘉宾简介

向青博士现为美国特拉华大学教授、国家海外杰出青年科学基金获得者、受聘为浙江大学永谦讲座教授、国际组合数学及其应用协会Fellow。主要研究方向为组合数学,擅长于使用深刻的代数和数论工具来研究组合设计,有限几何,编码和加法组合中的问题。现为国际组合数学界权威SCI期刊《The Electronic Journal of Combinatorics》主编之一,同时担任SCI期刊《Journal of Combinatorial Designs》、《Designs, Codes and Cryptography》、《Journal of Combinatorics and Number Theory》的编委。曾被授予由国际组合数学及其应用协会颁发的杰出青年学术成就奖—“Kirkman Medal”。

 

讲座简介:

Most combinatorial objects can be described by incidence, adjacency, or some other (0,1)-matrices. So one basic approach in combinatorics is to investigate combinatorial objects by using linear algebraic parameters (ranks over various fields, spectrum, Smith normal forms, etc.) of their corresponding matrices. In this talk, we will look at some successful examples of this approach; some examples are old, and some are new. In particular, we will talk about the recent bounds on the size of partial spreads of H(2d-1,q^2) and on the size of partial ovoids of the Ree-Tits octagon.