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:20260422T214705Z UID:YSseminar/1 DESCRIPTION:Title: Some quasi-isometric invariants for inverse semigroups\nby Diego Mar tínez (ICMAT - Institute of Mathematical Sciences) as part of York semigr oup seminar\n\n\nAbstract\nCoarse geometry is the study of metric spaces f rom a point of view far away\, that is\, up to coarse equivalence. Possibl y the most studied factory of examples are finitely generated groups\, whi ch are naturally equipped with the path length metric of their Cayley grap hs. One can then move onto the context of inverse semigroups where\, for v arious reasons we will detail\, one has to study its Schützenberger graph s. Properties of the semigroup that are invariant under coarse equivalence \, such as the growth type and the number of ends\, are here of particular interest.\n\nIn this talk we will be interested in two other properties\, namely amenability and property A. Amenability was introduced by Day in 1 957 as the existence of an invariant measure of the semigroup\, but it can be characterized from a geometric point of view in the Schützenberger gr aphs of the semigroup. Viewed from this point of view\, we will derive a c ertain necessary condition and prove that it's a quasi-isometric invariant . Much more recent is property A. In the talk we will define it and discus s its uses and possible characterizations\, mostly in relation with C*-alg ebras.\n\nThis is based on joint work with Fernando Lledó and Pere Ara.\n LOCATION:https://researchseminars.org/talk/YSseminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim Stokes (University of Waikato) DTSTART:20200513T103000Z DTEND:20200513T113000Z DTSTAMP:20260422T214705Z UID:YSseminar/2 DESCRIPTION:Title: How to generalise demonic composition\nby Tim Stokes (University of Waikato) as part of York semigroup seminar\n\n\nAbstract\nDemonic composit ion is defined on the set of binary relations over the non-empty set $X$\, $Rel_X$\, and is a variant of standard or ``angelic" composition. It ari ses naturally in the setting of the theory of non-deterministic computer p rograms\, and shares many of the nice features of ordinary composition (it is associative\, and generalises composition of functions). When equippe d with the operations of demonic composition and domain\, the resulting un ary semigroup defined on $Rel_X$ is a left restriction semigroup (like $PT _X$\, the semigroup of partial functions on $X$)\, whereas usual compositi on and domain give a unary semigroup satisfying weaker laws. \n\n\nBy con structing a constellation (a kind of ``one-sided" category)\, we show how this secondary demonic left restriction semigroup structure arises on $Rel _X$\, placing it in a more general context. The construction applies to a ny unary semigroup with a ``domain-like" operation satisfying certain mini mal conditions which we identify. \n\nIn particular it is shown that any Baer $*$-semigroup $S$ can be given a left restriction semigroup structure using the construction\, and that the result is even an inverse semigroup if $S$ is $*$-regular. It follows that the semigroup of $n\\times n$ mat rices over the real or complex numbers is an inverse semigroup with respec t to a modified notion of product that almost always agrees with the usual matrix product\, and in which inverse is pseudoinverse (Moore-Penrose inv erse).\n LOCATION:https://researchseminars.org/talk/YSseminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nora Szakacs (University of York) DTSTART:20200520T103000Z DTEND:20200520T113000Z DTSTAMP:20260422T214705Z 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\nAbstract\nIf $S$ is an inverse semigroup with a zero element\, the contracted semigroup algebra $K_0S$ is obtained from the semigroup algebra by identifying the zero of $S$ with the zero of the field. In the talk\, we examine when $K_0 S$ is simple. It is easy to see that $S$ congruence-free is a necessary co ndition\, as non-trivial congruences of $S$ give rise to non-trivial ideal s of $K_0S$. It has been known for long that this condition is not suffici ent however. Munn in the late 70's asked to characterize when a congruence -free inverse semigroup with zero has a simple contracted semigroup algebr a. A partial answer was given by Steinberg in 2016\, under the additional assumption that the inverse semigroup is Hausdorff. In the talk\, we prese nt a complete answer to Munn's question.\n LOCATION:https://researchseminars.org/talk/YSseminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hines (University of York) DTSTART:20200603T103000Z DTEND:20200603T113000Z DTSTAMP:20260422T214705Z UID:YSseminar/4 DESCRIPTION:Title: Elementary arithmetic as inverse semigroup theory\nby Peter Hines (U niversity of York) as part of York semigroup seminar\n\n\nAbstract\nThis t alk considers some very elementary arithmetic operations from the viewpoin t of inverse semigroup theory\, category theory\, and the theory of Cantor spaces. It starts by deriving monotone partial injections -- hence invers e semigroups -- from basic arithmetic operations\, and goes on to interpre t these as simple examples of well-known categorical properties and struct ures. This leads in a natural way to several very well-known inverse monoi ds\, and strict generalisations of these. These generalisations have a cl ose connection to elementary number-theory\, computability\, and formal un decidability.\n LOCATION:https://researchseminars.org/talk/YSseminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alfredo Costa (University of Coimbra) DTSTART:20200610T103000Z DTEND:20200610T113000Z DTSTAMP:20260422T214705Z UID:YSseminar/5 DESCRIPTION:Title: The profinite Schützenberger group defined by a symbolic dynamical syst em\nby Alfredo Costa (University of Coimbra) as part of York semigroup seminar\n\n\nAbstract\nIn finite semigroup theory\, free profinite semigr oups play a very\nimportant role. Around 2005\, Almeida introduced a conne ction with\nsymbolic dynamics that proved to be helpful to understand thei r\nstructure. One of the most relevant aspects of this connection is the\n association between an irreducible symbolic dynamical system X and the\nSc hützenberger group G(X) of a special regular J-class\, defined by X\, of\ nthe free profinite semigroup over the alphabet of X.\n\nThe profinite gro up 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 the profi nite completions of the fundamental groups of\nthe finite Rauzy graphs of X.\n\nIn this talk\, after introducing the basic concepts involved\, we su rvey some of the main results about the group G(X)\,\nending\, if time per mits\, with an application to the theory of codes.\n LOCATION:https://researchseminars.org/talk/YSseminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Tara Brough (Universidade NOVA de Lisboa) DTSTART:20200617T103000Z DTEND:20200617T113000Z DTSTAMP:20260422T214705Z UID:YSseminar/6 DESCRIPTION:Title: Context-free word problem semigroups\nby Tara Brough (Universidade N OVA de Lisboa) as part of York semigroup seminar\n\n\nAbstract\nI will giv e an overview of joint work with Alan Cain and Markus Pfeiffer on semigrou ps with context-free word problem\, covering at least the following:\n- Wh at does it mean for a semigroup to have context-free word problem?\n- Is t here a nice generalisation to semigroups of Muller and Schupp's famous res ult that a group has context-free word problem if and only if it is virtua lly free?\n- To what extent is the class of semigroups with context-free w ord problem closed under standard semigroup constructions (free product\, direct product\, Rees matrix etc.)?\n LOCATION:https://researchseminars.org/talk/YSseminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas-Quinn Gregson (TU Dresden) DTSTART:20201014T103000Z DTEND:20201014T113000Z DTSTAMP:20260422T214705Z UID:YSseminar/7 DESCRIPTION:Title: Solving equation systems in omega-categorical algebras\nby Thomas-Qu inn Gregson (TU Dresden) as part of York semigroup seminar\n\n\nAbstract\n We study the computational complexity of deciding whether a given set of t erm equalities and inequalities has a solution in an omega-categorical alg ebra $A$. There are omega-categorical groups where this problem is undecid able. We show that if $A$ is an omega-categorical semilattice or an abelia n group\, then the problem is in P or NP-hard. The hard cases are precisel y those where $Pol(A\,\\neq)$ is ``small'' (has a uniformly continuous min or-preserving map to the clone of projections on a two-element set). We re ly on the Barto-Pinsker theorem about the existence of pseudo-Siggers poly morphisms. To the best of our knowledge\, this is the first time that the pseudo-Siggers identity has been used to prove a complexity dichotomy.\n LOCATION:https://researchseminars.org/talk/YSseminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ganna Kudryavtseva (University of Ljubjana) DTSTART:20201028T113000Z DTEND:20201028T123000Z DTSTAMP:20260422T214705Z UID:YSseminar/8 DESCRIPTION:Title: Boolean inverse semigroups\nby Ganna Kudryavtseva (University of Lju bjana) as part of York semigroup seminar\n\n\nAbstract\nBoolean inverse se migroups are inverse semigroups whose idempotents admit a structure of a B oolean algebra and possessing joins of compatible pairs of elements. Non-c ommutative Stone duality connects Boolean inverse semigroups with Stone gr oupoids which are \\'etale topological groupoids whose space of identities is a Stone space. The focus of the talk will be on the speaker's recent w ork on $X$-to-join representations of inverse semigroups in Boolean invers e semigroups which are a relaxation of the notion of a cover-to-join repre sentation. We construct the universal $X$-to-join Booleanization of an in verse semigroup $S$ as a weakly meet-preserving quotient of the universal Booleanization ${\\mathrm B}(S)$ and show that all such quotients of ${\\ mathrm B}(S)$ arise via $X$-to-join representaions. As an application\, w e provide groupoid models for the intermediate boundary quotients of the $ C^*$-algebra of a Zappa-Szép product right LCM semigroup by Brownlowe\, Ramagge\, Robertson and Whittaker.\n LOCATION:https://researchseminars.org/talk/YSseminar/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hines DTSTART:20201111T113000Z DTEND:20201111T123000Z DTSTAMP:20260422T214705Z 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 introdu ction to inverse semigroup theory\, strongly motivated by its applications in other fields. No a priori knowledge of inverse semigroup theory is as sumed. \n\nStarting from the basic definitions\, we show how interesting a nd deep examples of inverse semigroups and related structures appear in ot her branches of mathematics\, and in computer science -- both theoretical and practical.\n\nFrom computer science\, we give examples ranging from ra ce conditions in computer security to Scott domains and Ladner's theorem. In pure mathematics\, we observe connections with structures such as Canto r Space\, (standard) Young tableaux\, Ballot sequences\, and Hilbert's hot el.\n\n(The two different classes of applications are of course closely co nnected).\n\n The ultimate aim is to provide some motivation for the study of (inverse) semigroup theory\, both in terms of its mathematical interes t\, and its practical applications.\n LOCATION:https://researchseminars.org/talk/YSseminar/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Francoeur (ENS Lyon) DTSTART:20201125T113000Z DTEND:20201125T123000Z DTSTAMP:20260422T214705Z UID:YSseminar/10 DESCRIPTION:Title: Free subsemigroups in automata semigroups\nby Dominik Francoeur (EN S Lyon) as part of York semigroup seminar\n\n\nAbstract\nOver the last few decades\, Mealy automata have been used to construct many groups and semi groups with interesting and exotic properties\, such as groups of intermed iate 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 explore one s uch connection between the automaton and the existence of free subsemigrou p in the corresponding semigroup. This is the result of a joint work with Ivan Mitrofanov.\n LOCATION:https://researchseminars.org/talk/YSseminar/10/ END:VEVENT END:VCALENDAR