BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Don Zagier (International Centre for Theoretical Physics) DTSTART:20211029T143000Z DTEND:20211029T160000Z DTSTAMP:20260423T004757Z UID:IMSAC/3 DESCRIPTION:Title: Fr om Knots to Number Theory II\nby Don Zagier (International Centre for Theoretical Physics) as part of IMSAC Distinguished Lecture Series\n\n\nAb stract\nFirst talk: https://www.youtube.com/watch?v=Moq1pJp0f9g\n\nAbstrac t\nDuring the course of the last few years a number of startling connectio ns between quantum invariants of knots and 3-manifolds and high-level numb er theory have emerged. Already the rigidity theorems of 3-dimensional hyp erbolic topology\, which have been known for many years\, had a quite non- trivial arithmetic content\, with the volume of every hyperbolic 3-manifol d being linked via the dilogarithm to the so-called Bloch group and algebr aic K-theory\, and another connection comes from the Kashaev invariant\, w hich is linked via his famous conjecture to the hyperbolic volume but also belongs to the so-called Habiro ring\, which is a beautiful number-theore tical object that is not yet well known to number theorists. The more rece nt developments that I will describe concern even deeper links to algebrai c number theory (construction of non-trivial units) and algebraic K-theory \, to a generalization of the classical Habiro ring to Habiro rings associ ated to arbitrary algebraic number fields\, and above all to surprising “quantum modularity” properties of the Kashaev invariant and its gener alizations leading to a new type of object in the theory of modular forms. All of the work that will be reported on is joint with Stavros Garoufalid is\, and some of it also with Rinat Kashaev and with Peter Scholze.\n\nThe lectures are intended for a general mathematical audience and do not requ ire any prior knowledge of knot theory\, K-theory\, modular forms theory\, or any other theory.\n LOCATION:https://researchseminars.org/talk/IMSAC/3/ END:VEVENT END:VCALENDAR