BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Frank Calegari (University of Chicago)\, Shiva Chidambaram (Univer
 sity of Chicago)\, and David P. Roberts (University of Minnesota\, Morris)
DTSTART:20200630T170000Z
DTEND:20200630T173000Z
DTSTAMP:20260423T200134Z
UID:ANTS14/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS14/6/">A
 belian surfaces with fixed 3-torsion</a>\nby Frank Calegari (University of
  Chicago)\, Shiva Chidambaram (University of Chicago)\, and David P. Rober
 ts (University of Minnesota\, Morris) as part of Algorithmic Number Theory
  Symposium (ANTS XIV)\n\n\nAbstract\nGiven a genus two curve $X\\colon y^2
 =x^5+ax^3+bx^2+cx+d$\, we give an explicit parametrization of all other su
 ch curves Y with a specified symplectic isomorphism on three-torsion of Ja
 cobians $\\mathrm{Jac}(X)[3]\\simeq \\mathrm{Jac}(Y)[3]$. It is known that
  under certain conditions modularity of $X$ implies modularity of infinite
 ly many of the $Y$\, and we explain how our formulas render this transfer 
 of modularity explicit. Our method centers on the invariant theory of the 
 complex reflection group $C_3\\times \\mathrm{Sp}_4(\\F_3)$. We discuss ot
 her examples where complex reflection groups are related to moduli spaces 
 of curves\, and in particular motivate our main computation with an exposi
 tion of the simpler case of the group\n\nChairs: Tom Fisher and Jen Paulhu
 s\n
LOCATION:https://researchseminars.org/talk/ANTS14/6/
END:VEVENT
END:VCALENDAR