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Membership problems in braid groups and Artin groups
- Speaker(s)
- Robert Gray
- Affiliation
- University of East Anglia
- Language of the talk
- English
- Date
- Oct. 23, 2025, 12:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1
- Information about the event
- referat online
- Seminar
- Seminar Algebra
In this talk I shall present some recent joint work with Carl-Fredrik Nyberg Brodda (KIAS, Seoul), in which we study several natural decision problems in braid groups and Artin groups. The subsemigroup membership problem for a group asks whether one can decide whether a given element of the group can be written as a product of some other finite set of elements of the group. In 2013, Potapov studied this problem for the braid group $B_n$ showing in particular that the problem is decidable when $n \leq 3$ and undecidable when $n \geq 5$. He left as an open problem the case of the four-strand braid group $B_4$. I will explain how we resolved this question for the braid group $B_4$ and how this then led us to prove a more general result that classifies the Artin groups with decidable subsemigroup membership problem. I shall also discuss several other related results, and open question, about other algorithmic problems for braid and Artin groups including the rational subset membership problem, semigroup intersection problem, and the identity problem.
