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: Rotary embeddings of Praeger-Xu graphs
Speaker: 刘鲁一 Luyi Liu (Southern University of Science and Technology)
Time: 16:00-17:00 (GMT+8), Wednesday September 17th
Location: Zoom: 262 780 8767 (passcode: gts2025)
Abstract:
Rotary maps (orientably regular maps) are highly symmetric graph embeddings on orientable surfaces. In this talk, we introduce the classification of rotary maps whose underlying graphs are Praeger-Xu graphs, denoted \(\operatorname{C}(p,r,s)\), for any odd prime \(p\) that does not divide \(r\).
We will establishe a one-to-one correspondence between the isomorphism classes of these maps and the multiplicity-free representations of the dihedral group \(\mathup{D}_{2r}\) over the finite field \(\mathbb{F}_p\). This work extends a recent classification for the case where \(p=2\).
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).