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报告题目：Applications of Combinatorial Nullstellensatz to graph colourings
报 告 人：朱绪鼎，浙江师范大学 教授
报告摘要：The Combinatorial Nullstellensatz gives a sufficient condition for a polynomial P(x1, x2, . . . , xn) ∈ F[x1, x2, . . . , xn] to have a non-zero point in a given grid S1×S2×. . .×Sn, where Si ⊆ F. Many combinatorial problems can be stated as the existence of a non-zero point of a polynomial in a certain grid, and hence have the potential of applying Combinatorial Nullstellensatz. This series of lectures explains some applications of Combinatorial Nullstellensatz to graph coloring and related problems. We focus on methods that show certain monomials in the expansion of a polynomial are non-vanishing, i.e., having non-zero coefficients. These include AlonTarsi orientations, interpolation formula and permanent method. These methods are illustrated with applications to problems in list colouring of graphs, vertex-edge weighting of graphs, list of forbidden out-degree orientations of graphs, etc.
报告人简介：朱绪鼎，浙江师范大学特聘教授，离散数学研究中心主任。1991年获得加拿大卡尔加里大学数学博士学位。曾任台湾中山大学西湾讲座教授。获得台湾科学委员会杰出研究奖，台湾数学学会学术奖，主持台湾杰出学者研究计划，2010年入选第三期国家高端人才计划。研究专长是图论、算法和组合优化。在SCI期刊发表论文300余篇，论文被引用3000余次(MathSciNet)。四十余次应邀在重要的国际学术会议上作大会报告。现任《J. Graph Theory》, 《European J. Combin.》，《Discrete. Mathematics》，《Contrib. Discrete Math.》，《Discuss. Math., Graph Theory》，《Bulletin of Academia Sinica》等国际学术期刊编委。
报告时间：2025年6月19日 14：30-16：00
报告地点：文渊楼B座B536
主办单位：数学与统计学院
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