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Welcome to the website for the 21st Postgraduate Group Theory Conference (PGTC) hosted at the University of Birmingham on 22nd – 26th July 2019. This will be the third time that the PGTC is hosted in Birmingham, with the previous incarnations being in 2002 and 2014. The PGTC is organised by postgraduate students to provide a friendly environment for other postgraduate students interested in Group Theory to talk about their work. Even though we encourage attending students to give a talk about their research, this is by no means compulsory.