BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carl-Fredrik Nyberg Brodda (KIAS) DTSTART:20240620T150500Z DTEND:20240620T160000Z DTSTAMP:20260423T003240Z UID:GaTO/105 DESCRIPTION:Title: F ree growth\, free counting\nby Carl-Fredrik Nyberg Brodda (KIAS) as pa rt of Geometry and topology online\n\nLecture held in Room B3.02 in the Ze eman Building\, University of Warwick.\n\nAbstract\nI will discuss some re cent forays into some counting problems for free objects. I will focus on free inverse semigroups and free regular ∗-semigroups. I will first disc uss recent results giving a precise rate of exponential growth of the free inverse monoid of arbitrary (finite) rank\, which turns out to be given b y a surprisingly complicated but algebraic number. I will then discuss a u seful tool for counting algebraic things – rewriting systems – and an elegant bijection which proves a surprising result about the rate of growt h of the monogenic free regular ∗-semigroup. Then\, and again using the theory of rewriting systems\, I will discuss just how non-finitely present ed some of these free objects are\, and some homological corollaries.\n\nT his is joint (in part) with M. Kambites\, N. Szakács\, and R. Webb.\n LOCATION:https://researchseminars.org/talk/GaTO/105/ END:VEVENT END:VCALENDAR