BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dilshan Wijesena (University of New South Wales) DTSTART:20230809T040000Z DTEND:20230809T050000Z DTSTAMP:20260423T021440Z UID:SiN/56 DESCRIPTION:Title: Irr educible Pythagorean representations of Thompson’s groups\nby Dilsha n Wijesena (University of New South Wales) as part of Symmetry in Newcastl e\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ are one of the most fascinating discrete infinite groups for their several unusual pr operties and their analytical properties have been challenging experts for many decades. One reason for this is because very little is known about i ts representation theory. Luckily\, thanks to the novel technology of Jone s\, a rich family of so-called Pythagorean unitary representation of Thomp son’s groups can be constructed by simply specifying a pair of finite-di mensional operators satisfying a certain equality. These representations c an even be extended to the celebrated Cuntz algebra and carry a powerful d iagrammatic calculus which we use to develop techniques to study their pro perties. This permits to reduce very difficult questions concerning irredu cibility and equivalence of infinite-dimensional representations into prob lems in finite-dimensional linear algebra. This provides a new rich class of irreducible representations of $F$. Moreover\, we introduce the Pythago rean dimension which is a new invariant for all representations of the Cun tz algebra and Pythagorean representations of $F\,T\,V$. For each dimensio n $d$\, we show the irreducible classes form a moduli space of a real mani fold of dimension $2d^2+1$.\n LOCATION:https://researchseminars.org/talk/SiN/56/ END:VEVENT END:VCALENDAR