讲座主题：A complete solution to the biased Alon-Krivelevich-Spencer-Szabo criterion problem for the discrepancy game

专家姓名：毛亚平

工作单位：青海师范大学

讲座时间：2026年06月23日 19:00-21:00

讲座地点：腾讯会议409-907-160

主办单位：烟台大学数学与信息科学学院

内容摘要：

Let H=(V,E) be a finite hypergraph. For positive integers p and q, the (p:q)-biased discrepancy game on H is played in complete rounds. In each round, Balancer first claims p previously unclaimed vertices, and then Unbalancer claims q previously unclaimed vertices. Let B and U be the final sets of vertices claimed by Balancer and Unbalancer, respectively.

For an edge e ∈ E, define D_e=q|B ∩ e|-p|U ∩ e|=(p+q)|B ∩ e|-p|e|. Thus D_e measures the deviation of Balancer＇s share of e from the density p/(p+q).

In 2005, Alon, Krivelevich, Spencer and Szabó proved a Chernoff-type potential criterion for the unbiased alternating discrepancy game, corresponding to the case p=q=1, and asked for a biased analogue for general p,q. In this talk, we give an affirmative answer of their problem and prove a complete biased analogue in the complete-round formulation.

More precisely, for every finite hypergraph H=(V,E) and every fixed bias (p:q), we give an explicit exponential condition under which Balancer has a strategy forcing -L_e^-≤D_e≤L_e^+ for every e ∈ E, where L_e^+ and L_e^- are prescribed edge-dependent target values. This is a joint work of Meiqin Wei and Gang Yang.

主讲人介绍：

毛亚平，博士毕业于南开大学，现任青海师范大学教授、博士生导师，中国数学会理事、青海省数学学会理事长。2020年获得日本学术振兴会国际项目（JSPS Fellow）。担任《International Journal of Interactive Multimedia and Artificial Intelligence》（SCI）等7个国际期刊编委，《Discrete Applied Mathematics》等3个期刊客座编辑。曾获全国青年教师教学竞赛三等奖、青海省优秀专家、省青年科技奖、省自然科学与工程技术优秀学科带头人、南开大学“研究生优秀毕业生”等10余项称号或奖励；入选青海省科技创新领军人才、省教学名师等人才计划。主持和主持完成国家和省部级科研项目14项；完全解决了Paul Erdős关于图拉姆齐有限性的两个猜想，完全解决了Ron Graham关于拉姆齐重数的重要猜想；完全解决了Noga Alon关于偏差游戏的公开问题；将Gallai-Ramsey理论发展到组合数论、偏序集、组合几何等领域，在《Journal of Combinatorial Theory, Series A》、《Information and Computation》等学术期刊发表论文80余篇，Springer出版学术专著2部，获得国家发明专利4项。