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Virtual, 12:00-15:00 UK time on 15-17 September 2021 This is the first edition of a twice-yearly workshop that will alternate between the Southampton Centre for Geometry, Topology and Applications and the Beijing Institute of Mathematical Sciences and Applications. The aims are to promote exciting new work in homotopy theory, with an emphasis on that by younger mathematicians, and to showcase the wide relevance of the subject to other areas of mathematics and science. Speakers: Steven Amelotte (ICERM) Guy Boyde (Southampton) Michael Farber (Queen Mary) Ruizhi Huang (Chinese Academy of Sciences) Norio Iwase (Kyushu) Pengcheng Li (Hebei) Abi Linton (Trondheim) Taras Panov (Moscow State) George Simmons (Southampton) Organisers: Stephen Theriault (Southampton) Jie Wu (Hebei)