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SUMMARY:Jordan Ellenberg (University of Wisconsin-Madison)
DTSTART:20201106T190000Z
DTEND:20201106T200000Z
DTSTAMP:20260404T094801Z
UID:SOQUAGAT/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SOQUA
 GAT/1/">Hyperbolic 3-manifolds and their covering spaces — some idle spe
 culation</a>\nby Jordan Ellenberg (University of Wisconsin-Madison) as par
 t of Series on open questions in Arithmetic\, Geometry and Topology\n\n\nA
 bstract\nI’ll talk about some asymptotic questions about towers of finit
 e covers of hyperbolic 3-manifolds\, especially those arising as the mappi
 ng cylinder of a pseudo-Anosov diffeomorphism of a surface. I will offer n
 o answers. Maybe you have some.\n
LOCATION:https://stable.researchseminars.org/talk/SOQUAGAT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20201120T170000Z
DTEND:20201120T180000Z
DTSTAMP:20260404T094801Z
UID:SOQUAGAT/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SOQUA
 GAT/2/">Expanding horocycles on the modular surface and some deep open pro
 blems in analytic number theory</a>\nby Claire Burrin (ETH Zurich) as part
  of Series on open questions in Arithmetic\, Geometry and Topology\n\n\nAb
 stract\nThe orbits of the horocycle flow on surfaces are classified: each 
 orbit is either dense or a closed horocycle around a cusp. Expanding close
 d horocycles are asymptotically dense\, and in fact become equidistributed
  on the surface. The precise rate of equidistribution is of interest\; on 
 the modular surface\, Zagier observed that a particular rate is equivalent
  to the Riemann hypothesis being true. In a recent preprint with Uri Shapi
 ra and Shucheng Yu\, we explored the asymptotic behavior of evenly spaced 
 points along an expanding closed horocycle on the modular surface. In this
  problem\, the number of sparse points is made to depend on the expansion 
 rate\, and the difficulty is that these points are no more invariant under
  the horocycle flow: Ratner’s theory does not apply. In this talk\, I wi
 ll sketch how this problem involves the theory of Diophantine approximatio
 n\, and estimates towards the Ramanujan conjecture for Hecke-Maass forms. 
 The goal is for this talk to be accessible for topologists\; no prior back
 ground in analytic number theory will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/SOQUAGAT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathleen Petersen (Florida State University)
DTSTART:20201204T170000Z
DTEND:20201204T180000Z
DTSTAMP:20260404T094801Z
UID:SOQUAGAT/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SOQUA
 GAT/3/">Symmetries and surface detection for $SL(2\,\\mathbb{C})$ characte
 r varieties of 3-manifolds</a>\nby Kathleen Petersen (Florida State Univer
 sity) as part of Series on open questions in Arithmetic\, Geometry and Top
 ology\n\n\nAbstract\nCuller\, Morgan\, and Shalen pioneered the detection 
 essential surfaces in 3-manifolds through $SL(2\,\\mathbb{C})$ character v
 arieties. I’ll discuss how symmetries of the 3-manifold affect this dete
 ction\, concluding with some examples. This is joint work with Jay Leach.\
 n
LOCATION:https://stable.researchseminars.org/talk/SOQUAGAT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benson Farb (University of Chicago)
DTSTART:20201211T190000Z
DTEND:20201211T200000Z
DTSTAMP:20260404T094801Z
UID:SOQUAGAT/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SOQUA
 GAT/4/">Hilbert's 13th problem and geometry</a>\nby Benson Farb (Universit
 y of Chicago) as part of Series on open questions in Arithmetic\, Geometry
  and Topology\n\n\nAbstract\nHilbert's 13th Problem (H13) is a fundamental
  open problem about polynomials in one variable.  It is part of a beautifu
 l (but mostly forgotten) story going back 3000 years.  In this talk I will
  explain how H13 (and related problems) fits into a wider framework that i
 ncludes problems in enumerative algebraic geometry and the theory of modul
 ar functions. I will then report on some recent progress\, joint with Mark
  Kisin and Jesse Wolfson.\n
LOCATION:https://stable.researchseminars.org/talk/SOQUAGAT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Reid (Rice University)
DTSTART:20201211T170000Z
DTEND:20201211T180000Z
DTSTAMP:20260404T094801Z
UID:SOQUAGAT/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/SOQUA
 GAT/5/">Where are the arithmetic homology spheres?</a>\nby Alan Reid (Rice
  University) as part of Series on open questions in Arithmetic\, Geometry 
 and Topology\n\n\nAbstract\nIn this talk we will discuss what is known abo
 ut the existence of arithmetic rational homology spheres\, as well as some
  conjectures on building others.\n
LOCATION:https://stable.researchseminars.org/talk/SOQUAGAT/5/
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