**Please note this seminar is in-person only SMRI ’What is ...?’ Seminar ’What is a cactus group?’ Iva Halacheva (Northeastern University) Thursday 3 August, 1:00-2:00pm (AEST) Carslaw 375 (in-person only) Abstract: The braid group is a classical algebraic object with an intuitively natural presentation via stacking pictures of braided strands. One point of view which makes them interesting to topologists is the interpretation of braid groups as the fundamental groups of certain configuration spaces. Braid groups also play a central role in representation theory through the Yang-Baxter equation, where they capture the symmetries of quantum group representations. The cactus group is a close relative of the braid group whose properties are yet to be fully explored. Cactus groups can also be viewed as the fundamental groups of interesting topological spaces and have recently been linked to combinatorial structures associated with quantum groups. I will describe the construction of the cactus group and outline some of the settings in which it appears. ---- Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on the SMRI Terrace (accessed through A14-04-L4.36) ---- Other upcoming SMRI events can be found here: https://mathematical-research-institute.sydney.edu.au/news-events/ SMRI YouTube Channel: https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI