讲座题目Topic: Global/local conjectures and character bounds in group representation theory

主办单位Organizer：三峡数学研究中心/Three Gorges Mathematical Research Center

报告专家Reporter: Nguyen Ngoc Hung, University of Akron

报告时间Date&Time (Chinese Time Zone)：2022.3.31, 9:00-11:00

报告地点Venue（线上Online）：Join Zoom Meeting

https://txstate.zoom.us/j/97791535907

Meeting ID: 977 9153 5907

专家简介 Brief Introduction of the Reporter：Nguyen Ngoc Hung has a Ph.D. in Mathematics from the University of Florida, USA, is an Associate Professor of Mathematics at University of Akron and has interests in finite group theory and representation theory. His recent research is on bounding the number of representations/characters of a finite group or its p-blocks.

摘要Report Summary：Group representation theory provides a way to study structure of groups via matrices. Born more than a century ago in the work of Frobenius and later developed by Burnside, Schur, Brauer, and others, it has become one of the most useful tools to study groups, with major success in several problems in group theory. Among the central problems nowadays in group representation theory are the so-called local-global conjectures, which predict that certain fundamental information on the representation theory of a finite group is encoded in its local subgroups. This talk consists of two parts. In the first part, I will introduce some of the most basic global/local conjectures such as the McKay conjecture, the McKay-Navarro conjecture, and the Alperin weight conjecture. In the second part, I will report on some of my recent work with my collaborators on problems, which naturally arise from the aforementioned local-global conjectures, on bounding the number of certain ordinary and modular characters/representations of a finite group or of a p-block of the group in terms of its p-local information.