BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gershom Bazerman DTSTART:20200429T170000Z DTEND:20200429T180000Z DTSTAMP:20260423T024512Z UID:ACTUCR/3 DESCRIPTION:Title: A localic approach to the semantics of dependency\, conflict\, and concurre ncy\nby Gershom Bazerman as part of ACT@UCR\n\n\nAbstract\nPetri nets have been of interest to applied category theory for some time. Back in th e 1980s\, one approach to their semantics was given by algebraic gadgets c alled "event structures." We use classical techniques from order theory to study event structures without conflict restrictions (which we term "depe ndency structures with choice") by their associated "traces"\, which let u s establish a one-to-one correspondence between DSCs and a certain class o f locales. These locales have an internal logic of reachability\, which ca n be equipped with "versioning" modalities that let us abstract away certa in unnecessary detail from an underlying DSC. With this in hand we can giv e a general notion of what it means to "solve a dependency problem" and co mbinatorial results bounding the complexity of this. Time permitting\, I w ill sketch work-in-progress which hopes to equip these locales with a noti on of conflict\, letting us capture the full semantics of general event st ructures in the form of homological data\, thus providing one avenue to th e topological semantics of concurrent systems. This is joint work with Ray mond Puzio.\n LOCATION:https://researchseminars.org/talk/ACTUCR/3/ END:VEVENT END:VCALENDAR