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SUMMARY:Michel Van Garrel (Birmingham)
DTSTART:20210121T100000Z
DTEND:20210121T110000Z
DTSTAMP:20260423T005806Z
UID:notts_ag/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/42/
 ">Stable maps to Looijenga pairs</a>\nby Michel Van Garrel (Birmingham) as
  part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nStart
  with a rational surface $Y$ admitting a decomposition of its anticanonica
 l divisor into at least 2 smooth nef components. We associate 5 curve coun
 ting theories to this Looijenga pair: 1) all genus stable log maps with ma
 ximal tangency to each boundary component\; 2) genus 0 stable maps to the 
 local Calabi-Yau surface obtained by twisting $Y$ by the sum of the line b
 undles dual to the components of the boundary\; 3) the all genus open Grom
 ov-Witten theory of a toric Calabi-Yau threefold associated to the Looijen
 ga pair\; 4) the Donaldson-Thomas theory of a symmetric quiver specified b
 y the Looijenga pair and 5) BPS invariants associated to the various curve
  counting theories. In this joint work with Pierrick Bousseau and Andrea B
 rini\, we provide closed-form solutions to essentially all of the associat
 ed invariants and show that the theories are equivalent. I will start by d
 escribing the geometric transitions from one geometry to the other\, then 
 give an overview of the curve counting theories and their relations. I wil
 l end by describing how the scattering diagrams of Gross and Siebert are a
  natural place to count stable log maps.\n
LOCATION:https://researchseminars.org/talk/notts_ag/42/
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