The use of geometric methods in group theory, in particular the investigation of geometric/topological properties of metric spaces naturally associated to groups has proven to be a very successful approach. Motivated by this, in the past couple of decades adventurous semigroup theorists and geometric group theorists have teamed up to develop similar methods for larger classes of semigroups. This has resulted in interesting and deep theories, including (but not limited to):

• a notion of quasi-isometry for monoids, and a corresponding version of the Švarc-Milnor lemma;
• a well-developed geometric approach to study inverse semigroup presentations, stemming from Stephen's procedure to solve the word problem using Stallings' foldings, which was fruitful in the case of one-relator inverse monoids, inverse  monoids presented by group reduced words, or sufficiently tree-like inverse monoids;
• a thorough  investigation of the properties F_n and FP_n of monoids using novel topological methods, and interesting applications to one-relator monoids;
• an exploration of semigroup amenability and its connections to geometry and Følner conditions, as well as to cogrowth and random walks;
• investigations of different notions of hyperbolicity for several  different  classes of semigroups;
• the theory of reflection  monoids, which are factorizable inverse monoids generated by partial reflections, generalizing the notion of reflection groups.

Some of the ideas developed for semigroups in turn yield new results in geometric group theory, such as a generalization of the Švarc-Milnor lemma, finding RAAGs in one-relator groups, or various  results about the submonoid membership problem in groups. Semigroups also come up naturally in the definition of near group actions.

At the same time, certain aspects of geometric (semi)group theory have come up in the study of C*-algebras. One way the three fields connect is through self-similarity. On the one hand, self-similar structures naturally give rise to inverse semigroups of isomorphisms between their substructures of different scales, whereas self-similar groups are one of the key objects of geometric group theory. Nekrashevych introduced C*-algebras associated to self-similar groups, which was also described as the universal C*-algebra for tight representations of an associated inverse semigroup. This inverse semigroup is exactly the inverse hull of the Zappa-Szép product of a free monoid and the group.
C*-algebras have also motivated the study of the amenability of inverse  semigroups, and the related, weaker condition of property A.

Yves de Cornulier (CNRS, University Lyon 1, FRA)
James East (Western Sydney University, AUS)
Brent Everitt (University of York, UK)
Martin Finn-Sell* (University of Vienna, AUT)
Alejandra Garrido (Universidad Autónoma de Madrid, ESP)
Robert Gray (University of East Anglia, UK)

Mark Kambites (University of Manchester, UK)
Nadia Larsen* (University of Oslo, NOR)
Carl-Fredrik Nyberg-Brodda (University of Manchester, UK)
John Meakin (University of Nebraska-Lincoln, USA)
Diego Martínez (Mathematical Institute, WWU Münster, GER)
Benjamin Steinberg* (City College of New York, USA)

*online speakers

The workshop is organized by Nóra Szakács, and is funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 799419.

Registration begins at 10:00 on June 20, in the Foyer of the Department of Environment Building. The talks take place in room B/B/006 of the Biology Building B. Coffee and lunch will be catered on all four days on campus. Click here for a map of all the locations, as color coded in the schedule.

The conference dinner will be held on Thursday (23rd) from 18:30 at the Cosy Club.

The event will be followed on June 24 by a one-day meeting of the North British Semigroups and Applications Network held at the same venue, which participants may be interested to stay for.

The workshop is held at the University of York, as a hybrid in-person/online event. Most presentations will be given in person at York, and some of our speakers will be giving remote talks. Everything will be broadcast on Zoom to allow for online participation.

The city of York

York is a lively English city located roughly halfway between London and Edinburgh. It is an attractive tourist destination with a large gothic cathedral, a nearly complete medieval city wall, and many pubs and restaurants. We recommend that in-person participants book their accommodation well in advance. Campus is easily reached from most parts of the city center by a direct bus link, or by a 30-45-minute walk. Several participants, including most speakers, will be staying at Staycity Aparthotels, which has very reasonable rates.

Getting to York

By plane: the closest airports to York are in Leeds (LBA), Doncaster (DSA) and Manchester (MAN). Out of the three, Manchester is often the most convenient as it has direct flights to many countries, and direct trains from the airport to York. From Leeds and Doncaster, you first take a bus to the railway station and then the train, but the train tickets can be cheaper than from Manchester.

By train: there is only one railway station in York, so you cannot miss it. One can buy train tickets online on websites like Trainline. PLEASE NOTE that there are railway strikes on the 21st, 23rd and 25th of June, so you will likely not be able to travel by rail these days. There seem to be limited services on the 19th as well.

By bus: this is, in general, a slower and less frequent option than the train (albeit cheaper), but due to railway strikes, I have included it. You can book your tickets here.