Hankel determinants: From human proofs to computer assisted proofs

主讲人:韩国牛教授 (University of Strasbourg and CNRS, France)
时间:2018年5月31日下午3:00   地点:N219

【摘要】In 1998, Allouche, Peyriere, Wen and Wen established a congruence relation between the Hankel determinants of the Thue-Morse sequence, and proved that all the Hankel determinants of the Thue-Morse sequence are nonzero. Similar properties for two other sequences, namely, the Gros sequence and the regular paperfolding sequence, were derived by Coons and Guo-Wu-Wen using the same method -- the human proof. In this talk, we present two computer assisted proofs, and show that the Hankel determinants of large classes of automatic sequences are nonzero or periodic. 

  This talk is dedicated to the memory of Prof. Wen-Tsun Wu (1919.05.12--2017.05.07) 

【报告人简介】韩国牛,1987年武汉大学毕业后到法国攻读博士学位,  师从著名组合学家 Dominique Foata. 1992获法国斯特拉斯堡大学 (University of Strasbourg)博士学位, 现为法国国家科学研究中心研究员。主要研究方向为组合数学、计算机代数、以及数论、代数问题中的算法研究。在整数分拆, 树结构, 自动序列的Hankel行列式等方面取得了一些列精彩的组合结果, 并在计算机辅助证明方面也造诣颇深。在国际组合数学高水平杂志《J. Combin. Theory Ser. A》,《Combinatorica》,《J. Algebraic Combin.》, 《European J. Combinatorics》,以及国际重要数学期刊 《Adv. Math.》,《Trans. Amer. Math. Soc.》, 《Inter. Math. Research Notices》等发表学术论文100余篇.