报告题目：Big Ramsey degrees of universal structures

报告人：Jan Hubička，Charles University

报告时间：2025年6月27日（周五）15:00-16:00

报告地点：20-306

报告摘要：A structure M is said to have finite big Ramsey degrees if for any of its finite substructures A, there exists a number BRD(M,A) such that for any finite coloring of the copies of A within M, one can find a copy of M in M that uses at most BRD(A,M) colors.  Denoting by N the set of all integers seen as an linearly ordered set, by the classical infinite Ramsey theorem, for every finite order O it holds that BRD(O,N)=1. The study of big Ramsey degrees was initiated in 1960's by results of  Sierpinski, Galvin, Devlin and Laver on coloring suborders of the order  of rationals. Recently the area has been revitalized with number of new results.  In this talk I will introduce the main concepts and dicuss a new proof technique which can be used to show that every countable universal triangle-free graph has finite big Ramsey degree.

报告人简介：Jan Hubička博士是捷克查理大学应用数学系副教授，同时也是SUSE软件公司的开发者。他的研究方向包括结构Ramsey理论、图同态以及齐性结构等。他在Proc. Lond. Math. Soc.、Adv. Math.、Trans. Amer. Math. Soc.、Combinatorica、J. Combin. Theory Ser. B、J. Combin. Theory Ser. A、Adv. Comb. 等期刊发表论文30余篇。 此外，Jan博士是GNU编译器集合（GCC）项目的长期贡献者，曾实现对x86-64架构的初始移植工作，并维护跨过程优化、基于反馈的优化以及i386架构的支持。他也对摄影史有浓厚兴趣，致力于Šechtl与Voseček工作室历史影像档案的数字化工作。

邀请人：朱绪鼎