BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Diego Martínez (ICMAT - Institute of Mathematical Sciences) DTSTART:20200506T103000Z DTEND:20200506T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/1 DESCRIPTION:Title: Some quasi-isometric invariants for inverse semigroups\nby Di ego Martínez (ICMAT - Institute of Mathematical Sciences) as part of York semigroup seminar\n\n\nAbstract\nCoarse geometry is the study of metric s paces from a point of view far away\, that is\, up to coarse equivalence. Possibly the most studied factory of examples are finitely generated group s\, which are naturally equipped with the path length metric of their Cayl ey graphs. One can then move onto the context of inverse semigroups where\ , for various reasons we will detail\, one has to study its Schützenberge r graphs. Properties of the semigroup that are invariant under coarse equi valence\, such as the growth type and the number of ends\, are here of par ticular interest.\n\nIn this talk we will be interested in two other prope rties\, namely amenability and property A. Amenability was introduced by D ay in 1957 as the existence of an invariant measure of the semigroup\, but it can be characterized from a geometric point of view in the Schützenbe rger graphs of the semigroup. Viewed from this point of view\, we will der ive a certain necessary condition and prove that it's a quasi-isometric in variant. Much more recent is property A. In the talk we will define it and discuss its uses and possible characterizations\, mostly in relation with C*-algebras.\n\nThis is based on joint work with Fernando Lledó and Pere Ara.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim Stokes (University of Waikato) DTSTART:20200513T103000Z DTEND:20200513T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/2 DESCRIPTION:Title: How to generalise demonic composition\nby Tim Stokes (Univers ity of Waikato) as part of York semigroup seminar\n\n\nAbstract\nDemonic c omposition is defined on the set of binary relations over the non-empty se t $X$\, $Rel_X$\, and is a variant of standard or ``angelic" composition. It arises naturally in the setting of the theory of non-deterministic com puter programs\, and shares many of the nice features of ordinary composit ion (it is associative\, and generalises composition of functions). When equipped with the operations of demonic composition and domain\, the resul ting unary semigroup defined on $Rel_X$ is a left restriction semigroup (l ike $PT_X$\, the semigroup of partial functions on $X$)\, whereas usual co mposition and domain give a unary semigroup satisfying weaker laws. \n\n\ nBy constructing a constellation (a kind of ``one-sided" category)\, we sh ow how this secondary demonic left restriction semigroup structure arises on $Rel_X$\, placing it in a more general context. The construction appli es to any unary semigroup with a ``domain-like" operation satisfying certa in minimal conditions which we identify. \n\nIn particular it is shown th at any Baer $*$-semigroup $S$ can be given a left restriction semigroup st ructure using the construction\, and that the result is even an inverse se migroup if $S$ is $*$-regular. It follows that the semigroup of $n\\times n$ matrices over the real or complex numbers is an inverse semigroup with respect to a modified notion of product that almost always agrees with th e usual matrix product\, and in which inverse is pseudoinverse (Moore-Penr ose inverse).\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nora Szakacs (University of York) DTSTART:20200520T103000Z DTEND:20200520T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/3 DESCRIPTION:Title: Simplicity of contracted inverse semigroup algebras\nby Nora Szakacs (University of York) as part of York semigroup seminar\n\n\nAbstra ct\nIf $S$ is an inverse semigroup with a zero element\, the contracted se migroup algebra $K_0S$ is obtained from the semigroup algebra by identifyi ng the zero of $S$ with the zero of the field. In the talk\, we examine wh en $K_0S$ is simple. It is easy to see that $S$ congruence-free is a neces sary condition\, as non-trivial congruences of $S$ give rise to non-trivia l ideals of $K_0S$. It has been known for long that this condition is not sufficient however. Munn in the late 70's asked to characterize when a con gruence-free inverse semigroup with zero has a simple contracted semigroup algebra. A partial answer was given by Steinberg in 2016\, under the addi tional assumption that the inverse semigroup is Hausdorff. In the talk\, w e present a complete answer to Munn's question.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hines (University of York) DTSTART:20200603T103000Z DTEND:20200603T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/4 DESCRIPTION:Title: Elementary arithmetic as inverse semigroup theory\nby Peter H ines (University of York) as part of York semigroup seminar\n\n\nAbstract\ nThis talk considers some very elementary arithmetic operations from the v iewpoint of inverse semigroup theory\, category theory\, and the theory of Cantor spaces. It starts by deriving monotone partial injections -- hence inverse semigroups -- from basic arithmetic operations\, and goes on to i nterpret these as simple examples of well-known categorical properties and structures. This leads in a natural way to several very well-known invers e monoids\, and strict generalisations of these. These generalisations ha ve a close connection to elementary number-theory\, computability\, and fo rmal undecidability.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alfredo Costa (University of Coimbra) DTSTART:20200610T103000Z DTEND:20200610T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/5 DESCRIPTION:Title: The profinite Schützenberger group defined by a symbolic dynamic al system\nby Alfredo Costa (University of Coimbra) as part of York se migroup seminar\n\n\nAbstract\nIn finite semigroup theory\, free profinite semigroups play a very\nimportant role. Around 2005\, Almeida introduced a connection with\nsymbolic dynamics that proved to be helpful to understa nd their\nstructure. One of the most relevant aspects of this connection i s the\nassociation between an irreducible symbolic dynamical system X and the\nSchützenberger group G(X) of a special regular J-class\, defined by X\, of\nthe free profinite semigroup over the alphabet of X.\n\nThe profin ite group G(X) is a dynamical invariant. In the case of\nminimal systems\, it has a sort of geometric interpretation: it is the\ninverse limit of th e profinite completions of the fundamental groups of\nthe finite Rauzy gra phs of X.\n\nIn this talk\, after introducing the basic concepts involved\ , we survey some of the main results about the group G(X)\,\nending\, if t ime permits\, with an application to the theory of codes.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Tara Brough (Universidade NOVA de Lisboa) DTSTART:20200617T103000Z DTEND:20200617T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/6 DESCRIPTION:Title: Context-free word problem semigroups\nby Tara Brough (Univers idade NOVA de Lisboa) as part of York semigroup seminar\n\n\nAbstract\nI w ill give an overview of joint work with Alan Cain and Markus Pfeiffer on s emigroups with context-free word problem\, covering at least the following :\n- What does it mean for a semigroup to have context-free word problem?\ n- Is there a nice generalisation to semigroups of Muller and Schupp's fam ous result that a group has context-free word problem if and only if it is virtually free?\n- To what extent is the class of semigroups with context -free word problem closed under standard semigroup constructions (free pro duct\, direct product\, Rees matrix etc.)?\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas-Quinn Gregson (TU Dresden) DTSTART:20201014T103000Z DTEND:20201014T113000Z DTSTAMP:20260404T095717Z UID:YSseminar/7 DESCRIPTION:Title: Solving equation systems in omega-categorical algebras\nby Th omas-Quinn Gregson (TU Dresden) as part of York semigroup seminar\n\n\nAbs tract\nWe study the computational complexity of deciding whether a given s et of term equalities and inequalities has a solution in an omega-categori cal algebra $A$. There are omega-categorical groups where this problem is undecidable. We show that if $A$ is an omega-categorical semilattice or an abelian group\, then the problem is in P or NP-hard. The hard cases are p recisely those where $Pol(A\,\\neq)$ is ``small'' (has a uniformly continu ous minor-preserving map to the clone of projections on a two-element set) . We rely on the Barto-Pinsker theorem about the existence of pseudo-Sigge rs polymorphisms. To the best of our knowledge\, this is the first time th at the pseudo-Siggers identity has been used to prove a complexity dichoto my.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ganna Kudryavtseva (University of Ljubjana) DTSTART:20201028T113000Z DTEND:20201028T123000Z DTSTAMP:20260404T095717Z UID:YSseminar/8 DESCRIPTION:Title: Boolean inverse semigroups\nby Ganna Kudryavtseva (University of Ljubjana) as part of York semigroup seminar\n\n\nAbstract\nBoolean inv erse semigroups are inverse semigroups whose idempotents admit a structure of a Boolean algebra and possessing joins of compatible pairs of elements . Non-commutative Stone duality connects Boolean inverse semigroups with S tone groupoids which are \\'etale topological groupoids whose space of ide ntities is a Stone space. The focus of the talk will be on the speaker's r ecent work on $X$-to-join representations of inverse semigroups in Boolean inverse semigroups which are a relaxation of the notion of a cover-to-joi n representation. We construct the universal $X$-to-join Booleanization o f an inverse semigroup $S$ as a weakly meet-preserving quotient of the uni versal Booleanization ${\\mathrm B}(S)$ and show that all such quotients of ${\\mathrm B}(S)$ arise via $X$-to-join representaions. As an applicat ion\, we provide groupoid models for the intermediate boundary quotients o f the $C^*$-algebra of a Zappa-Szép product right LCM semigroup by Brown lowe\, Ramagge\, Robertson and Whittaker.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hines DTSTART:20201111T113000Z DTEND:20201111T123000Z DTSTAMP:20260404T095717Z UID:YSseminar/9 DESCRIPTION:Title: Inverse Semigroups and Their Applications\nby Peter Hines as part of York semigroup seminar\n\n\nAbstract\nThis talk is intended as an introduction to inverse semigroup theory\, strongly motivated by its appli cations in other fields. No a priori knowledge of inverse semigroup theor y is assumed. \n\nStarting from the basic definitions\, we show how intere sting and deep examples of inverse semigroups and related structures appea r in other branches of mathematics\, and in computer science -- both theor etical and practical.\n\nFrom computer science\, we give examples ranging from race conditions in computer security to Scott domains and Ladner's th eorem. In pure mathematics\, we observe connections with structures such a s Cantor Space\, (standard) Young tableaux\, Ballot sequences\, and Hilber t's hotel.\n\n(The two different classes of applications are of course clo sely connected).\n\n The ultimate aim is to provide some motivation for th e study of (inverse) semigroup theory\, both in terms of its mathematical interest\, and its practical applications.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Francoeur (ENS Lyon) DTSTART:20201125T113000Z DTEND:20201125T123000Z DTSTAMP:20260404T095717Z UID:YSseminar/10 DESCRIPTION:Title: Free subsemigroups in automata semigroups\nby Dominik Franco eur (ENS Lyon) as part of York semigroup seminar\n\n\nAbstract\nOver the l ast few decades\, Mealy automata have been used to construct many groups a nd semigroups with interesting and exotic properties\, such as groups of i ntermediate growth or infinite finitely generated periodic groups. One can wonder how the properties of an automaton are reflected in the properties of the semigroup or group that it generates. In this talk\, I will explor e one such connection between the automaton and the existence of free subs emigroup in the corresponding semigroup. This is the result of a joint wor k with Ivan Mitrofanov.\n LOCATION:https://stable.researchseminars.org/talk/YSseminar/10/ END:VEVENT END:VCALENDAR