Algebra seminar - Justin Lynd
| Dates: | 4 March 2025 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Justin Lynd |
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Title: Partial groups and higher Segal conditions
Abstract: A partial group is a set together with a multivariable product that is only defined on certain "multipliable" words of the underlying set. They were defined by Chermak in order to study linking systems of saturated fusion systems from a more group theoretic point of view. Partial groupoids are probably best thought of as certain types of symmetric simplicial sets, presheaves on the category of nonempty finite sets and all functions. This point of view allows one to form colimits of partial groups in a concrete way and construct lots of examples. In addition it suggests a notion of higher associativity of a partial group in the form of the higher Segal conditions of Dyckeroff and Kapranov. We develop tools to understand these associativity conditions and then carry out explicit computations of the degree of associativity of partial groups in concrete settings, such as for punctured Weyl groups. This is joint work with Philip Hackney.
Speaker
Justin Lynd
Organisation: University of Louisiana at Lafayette
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Frank Adams 1
Alan Turing Building
Manchester
