BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vladimir Kazakov (ENS Paris) DTSTART:20210610T141500Z DTEND:20210610T160000Z DTSTAMP:20260423T040335Z UID:LIJC/46 DESCRIPTION:Title: Du ally weighted graphs and 2d quantum gravity\nby Vladimir Kazakov (ENS Paris) as part of London Integrability Journal Club\n\n\nAbstract\nDually weighted graphs (DWG) are planar Feynman graphs bearing two sets of coup lings: one set of usual couplings $t_n$ attached to the vertices of valen ce $n$\, and another set of dual couplings $t_n^*$ attached to the faces (dual vertices) of valence $n$. Such couplings allow a deep control on possible shapes of planar graphs. For example\, if one turns on only th e couplings $t_4$ and $t_4^*$ the graph takes a "fishnet form" of a regu lar square lattice. The problem of counting of such graphs can be formulat ed as a modified hermitian one matrix model with an extra constant matrix. The partition function can be then represented in terms of the "character expansion" over Young tableaux\, solvable by the saddle point approximat ion. I will review old results on DWG from my papers with M.Staudacher and Th.Wynter\, including the techniques of computing Schur characters of a large Young tableau and deriving the elliptic algebraic curve for coun ting of planar quadrangulations. Then I will present new results from our ongoing work with F.Levkovich-Maslyuk where we count the disc quadrangu lations with large\, macroscopic area and boundary. This allows to extract interesting continuous limit of fluctuating 2d geometry\, interpolating between the "almost" flat disc with a few dynamical conical defects and the disc partition function for pure 2d quantum gravity\, generalizing old results for the spherical topology.\n LOCATION:https://researchseminars.org/talk/LIJC/46/ END:VEVENT END:VCALENDAR