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BEGIN:VEVENT
SUMMARY:Michelle Manes (UH/NSF)
DTSTART:20200926T160500Z
DTEND:20200926T165500Z
DTSTAMP:20260415T132045Z
UID:FRNTDFall2020/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FRNTDFall202
 0/1/">Complex multiplication in arithmetic dynamics</a>\nby Michelle Manes
  (UH/NSF) as part of Front Range Number Theory Day\n\n\nAbstract\nArithmet
 ic dynamics is the study of number theoretic properties of iterated functi
 ons.\nThe field draws inspiration from dynamical analogues of theorems and
  conjectures in classical\narithmetic geometry. In this talk\, I will desc
 ribe some of these analogues with a focus on\nattempts to develop a “dyn
 amical” theory of complex multiplication.\n
LOCATION:https://researchseminars.org/talk/FRNTDFall2020/1/
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BEGIN:VEVENT
SUMMARY:Andrew Sutherland (MIT)
DTSTART:20200926T191500Z
DTEND:20200926T200500Z
DTSTAMP:20260415T132045Z
UID:FRNTDFall2020/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FRNTDFall202
 0/2/">Sato-Tate groups of abelian threefolds</a>\nby Andrew Sutherland (MI
 T) as part of Front Range Number Theory Day\n\n\nAbstract\nLet $A$ be an a
 belian variety of dimension $g$ defined over a\nnumber field $K$. As defin
 ed by Serre\, the Sato-Tate group $\\mathrm{ST}(A)$ is a\ncompact subgroup
  of the unitary symplectic group $\\mathrm{USp}(2g)$ equipped with\na map 
 that sends each Frobenius element of the absolute Galois group\nof $K$ at 
 primes $\\mathfrak p$ of good reduction for $A$ to a conjugacy class of $\
 \mathrm{ST}(A)$\nwhose characteristic polynomial is determined by the zeta
  function of\nthe reduction of $A$ at $\\mathfrak p$. Under a set of axiom
 s proposed by Serre that\nare known to hold for $g \\le 3$\, up to conjuga
 cy in $\\mathrm{Usp}(2g)$ there is a\nfinite list of possible Sato-Tate gr
 oups that can arise for abelian\nvarieties of dimension $g$ over number fi
 elds.\n\nFor $g = 1$ there are $3$ possibilities for $\\mathrm{ST}(A)$\, f
 or $g = 2$ there are\n$52$\, and last year it was shown that for $g = 3$ t
 here are $410$. In this\ntalk I will give a brief overview of this classif
 ication and then\ndiscuss ongoing efforts to produce explicit examples tha
 t realize\nthese $410$ possibilities.\n\nThis is joint work with Kiran Ked
 laya and Francesc Fité\n
LOCATION:https://researchseminars.org/talk/FRNTDFall2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christelle Vincent (UVM)
DTSTART:20200926T202000Z
DTEND:20200926T211000Z
DTSTAMP:20260415T132045Z
UID:FRNTDFall2020/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FRNTDFall202
 0/3/">Computing hyperelliptic invariants from period matrices</a>\nby Chri
 stelle Vincent (UVM) as part of Front Range Number Theory Day\n\n\nAbstrac
 t\nIn this talk we present an obstacle to computing invariants of curves w
 hose Jacobian\nhas CM (complex multiplication)\, when the genus of the cur
 ve is greater than 1. The problem is\nessentially that while the Jacobian 
 has everywhere potential good reduction\, the curve does not.\nWe show the
  connection between this obstacle and a certain embedding problem which we
 \ndefine in the talk\, and present our progress on analyzing the embedding
  problem. This is joint\nwork with Ionica\, Kilicer\, Lauter\, Lorenzo Gar
 cia and Manzateanu.\n
LOCATION:https://researchseminars.org/talk/FRNTDFall2020/3/
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