报告人：Apostolos Tzimoulis

工作单位：School of Business and Economics, Vrije Universiteit Amsterdam

报告时间：4月1日（周二），14:00 – 15:30

地点：知新楼B1044

题目：Tutorial in Birkhoff's theorem on universal algebra

摘要：This tutorial is designed to introduce bachelor-level mathematics students to the foundational concepts of universal algebra and to explore one of its cornerstone results: Birkhoff's HSP Theorem. We will begin by defining key notions such as algebras, homomorphisms, subalgebras, direct products, and equational classes. With these tools in hand, we will state and prove Birkhoff's Theorem, which establishes that a class of algebras is a variety, that is defined by a set of equations, if and only if it is closed under homomorphic images, subalgebras, and direct products. Through the proof we will introduce key notions of universal algebra and highlight the interplay between algebraic constructions and equational logic. No prior knowledge of universal algebra is required, making this tutorial accessible to students with a basic background in algebra and mathematical reasoning.

个人简介：Apostolos Tzimoulis is a mathematical logician and researcher at the University of Luxembourg. He holds a PhD in Applied Logic from Delft University of Technology and specializes in algebraic logic, proof theory, formal methods, and their applications in artificial intelligence. His research explores the mathematical foundations of logic, contributing to both theoretical advancements and practical applications. Previously, he was an assistant professor at the School of Business and Economics at the Vrije Universiteit Amsterdam.