这是群论和图论方向的线上系列报告，我们希望能够促进国内外青年学者（博士生为主）在群论和图论研究上的交流。报告主题分布在（但不限于）以下研究方向：
This is a platform for young group theorists and graph theorists (mostly PhD students) to talk about their research and related topics online. The topic can be anything related to group theory and graph theory, including but not limited to the following.
一般地，系列报告定期于北京时间每周三下午16:00-17:00进行。
Our usual time is Wednesday 16:00-17:00 (GMT+8).
Title: An algebraic approach to Baranyai's wreath conjecture
Speaker: Jan Petr (University of Cambridge)
Time: 16:00-17:00 (GMT+8), Wednesday June 4th
Location: Zoom: 262 780 8767 (passcode: gts2025)
Abstract:
In 1970s, Baranyai showed that every \(k\)-uniform complete hypergraph of \(n\) such that \(k \mid n\) can be decomposed into perfect matchings, thus confirming a long-standing conjectured generalization of Kirkman's schoolgirl problem. At the end of his paper, he conjectured an even stronger statement, the "wreath conjecture". To this day, it is open. Katona wrote about the wreath conjecture: "This conjecture [...] seems to be too algebraic. One does not expect to solve it without algebra. (Unless it is not true.)”
In this talk, we look at an algebraic approach to the conjecture, analyzing a matrix encoding the problem. We discuss the properties of the matrix, as well as how other decomposition problems can be approached in this way.
The talk is based on joint work with Pavel Turek.
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).