*主持人：周国栋 教授

*讲座内容简介：
Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking an uniform approach, this paper gives an operadic study of compatibility conditions for nonsymmetric operads with unary and binary operations, and homogeneous quadratic and cubic relations. This generalizes the previous studies for binary quadratic operads. We consider three compatibility conditions, namely the linear compatibility, matching compatibility and total compatibility, with increasingly strict restraints among the replicated copies. The linear compatibility is in Koszul dual to the total compatibility, while the matching compatibility is self dual. Further, each compatibility can be expressed in terms of either one or both of the two Manin square products.

*主讲人简介：
高兴，博士，兰州大学教授、博士生导师。于2010年7月在兰州大学数学与统计学院获得博士学位，留校工作至今。在2015年8月至2016年8月间，在美国Rutgers大学交流访问，师从Rota-Baxter代数的国际领军人物郭锂教授。主要从事Rota-Baxter代数和代数组合等领域的研究， 在Journal of Algebra、 Journal of Pure and Applied Algebra 等国际期刊上发表SCI学术论文四十余篇。主持数学天元基金、青年科学基金、国家自然科学基金面上项目和甘肃省自然科学基金项目, 曾参与国家自然科学基金项目2项和甘肃省自然科学基金项目1项，出版专著一本。