BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nathan Reading (North Carolina State University) DTSTART:20210119T160000Z DTEND:20210119T170000Z DTSTAMP:20260423T052447Z UID:OCAS/13 DESCRIPTION:Title: Th eta functions and the mutation fan\nby Nathan Reading (North Carolina State University) as part of Online Cluster Algebra Seminar (OCAS)\n\n\nAb stract\nThe setting for this work is the cluster scattering diagram define d by\nGross\, Hacking\, Keel\, and Kontsevich (GHKK).  The cluster scatte ring\ndiagram is a collection of walls (codimension-1 cones plus some\nadd itional algebraic data).  Theta functions (one for each g-vector)\ninclud e the cluster monomials and form a basis for the cluster algebra\n(or ofte n something larger).  Explicit constructions of cluster\nscattering diagr ams and explicit computations of theta functions are\nhopelessly complicat ed in general\, but I believe that eventually there\nwill be combinatorial models in all mutation-finite types.  I'll\nmention work with Salvatore Stella on combinatorial models in affine\ntype\, and work with Greg Muller and Shira Viel on the surfaces case.\nBut I will spend most of the time d iscussing a result (with Stella)\nthat I think will make it possible to co mplete these combinatorial\nconstructions of theta functions.\n\nThe mutat ion fan encodes the piecewise-linear geometry of matrix\nmutation.  The r esult is:  If you take a product of theta functions\nwhose g-vectors are all in one cone of the mutation fan\, the product\nexpands as a sum of the ta functions whose g-vectors are all in one\ncone of the mutation fan.  T he result seems natural and in some sense\nunsurprising\, but it requires some work and it is quite useful.  The\nresult requires two serious chang es in point of view from the GHKK\nsetup:  Taking a different point of vi ew on what "mutation of\nscattering diagrams" means and demoting "frozen v ariables" to the\nstatus of coefficients.\n LOCATION:https://researchseminars.org/talk/OCAS/13/ END:VEVENT END:VCALENDAR