BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Daniel Douglas (Yale University)
DTSTART:20220217T220000Z
DTEND:20220217T233000Z
DTSTAMP:20260423T005728Z
UID:PIMS_GAP/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PIMS_GAP/1/"
 >Tropical Fock-Goncharov coordinates for SL_3-webs on surfaces</a>\nby Dan
 iel Douglas (Yale University) as part of PIMS Geometry / Algebra / Physics
  (GAP) Seminar\n\n\nAbstract\nFor a finite-type surface $\\mathfrak{S}$\, 
 we study a preferred basis for the commutative algebra $\\mathbb{C}[\\math
 cal{R}_{\\mathrm{SL}_3}(\\mathfrak{S})]$ of regular functions on the $\\te
 xt{SL}_3(\\mathbb C)$-character variety\, introduced by Sikora-Westbury. T
 hese basis elements come from the trace functions associated to certain tr
 i-valent graphs embedded in the surface $\\mathfrak{S}$. We show that this
  basis can be naturally indexed by positive integer coordinates\, defined 
 by Knutson-Tao rhombus inequalities and modulo $3$ congruence conditions. 
 These coordinates are related\, by the geometric theory of Fock-Goncharov\
 , to the tropical points at infinity of the dual version of the character 
 variety. This is joint work with Zhe Sun.\n
LOCATION:https://researchseminars.org/talk/PIMS_GAP/1/
END:VEVENT
END:VCALENDAR