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SUMMARY:Tom Ducat (Imperial)
DTSTART:20200513T120000Z
DTEND:20200513T130000Z
DTSTAMP:20260423T041342Z
UID:notts_ag/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/4/"
 >A Laurent phenomenon for $\\mathrm{OGr}(5\,10)$ and explicit mirror symme
 try for the Fano $3$-fold $V_{12}$</a>\nby Tom Ducat (Imperial) as part of
  Online Nottingham algebraic geometry seminar\n\n\nAbstract\nThe $5$-perio
 dic birational map $(x\, y) -> (y\, (1+y)/x)$ can be interpreted as a muta
 tion between five open torus charts in a del Pezzo surface of degree $5$\,
  coming from a cluster algebra structure on the Grassmannian $\\mathrm{Gr}
 (2\,5)$. This can used to construct a rational elliptic fibration which is
  the Landau-Ginzburg mirror to $\\mathrm{dP}_5$. I will briefly recap this
 \, and then explain the following $3$-dimensional generalisation: the $8$-
 periodic birational map $(x\, y\, z) -> (y\, z\, (1+y+z)/x)$ can be used t
 o exhibit a Laurent phenomenon for the orthogonal Grassmannian $\\mathrm{O
 Gr}(5\,10)$ and construct a completely explicit $K3$ fibration which is mi
 rror to the Fano $3$-fold $V_{12}$\, as well as some other Fano $3$-folds.
 \n
LOCATION:https://researchseminars.org/talk/notts_ag/4/
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