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SUMMARY:Jordan Ellenberg (University of Wisconsin-Madison)
DTSTART:20201106T190000Z
DTEND:20201106T200000Z
DTSTAMP:20260422T225823Z
UID:SOQUAGAT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SOQUAGAT/1/"
 >Hyperbolic 3-manifolds and their covering spaces — some idle speculatio
 n</a>\nby Jordan Ellenberg (University of Wisconsin-Madison) as part of Se
 ries on open questions in Arithmetic\, Geometry and Topology\n\n\nAbstract
 \nI’ll talk about some asymptotic questions about towers of finite cover
 s of hyperbolic 3-manifolds\, especially those arising as the mapping cyli
 nder of a pseudo-Anosov diffeomorphism of a surface. I will offer no answe
 rs. Maybe you have some.\n
LOCATION:https://researchseminars.org/talk/SOQUAGAT/1/
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BEGIN:VEVENT
SUMMARY:Claire Burrin (ETH Zurich)
DTSTART:20201120T170000Z
DTEND:20201120T180000Z
DTSTAMP:20260422T225823Z
UID:SOQUAGAT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SOQUAGAT/2/"
 >Expanding horocycles on the modular surface and some deep open problems i
 n analytic number theory</a>\nby Claire Burrin (ETH Zurich) as part of Ser
 ies on open questions in Arithmetic\, Geometry and Topology\n\n\nAbstract\
 nThe orbits of the horocycle flow on surfaces are classified: each orbit i
 s either dense or a closed horocycle around a cusp. Expanding closed horoc
 ycles are asymptotically dense\, and in fact become equidistributed on the
  surface. The precise rate of equidistribution is of interest\; on the mod
 ular surface\, Zagier observed that a particular rate is equivalent to the
  Riemann hypothesis being true. In a recent preprint with Uri Shapira and 
 Shucheng Yu\, we explored the asymptotic behavior of evenly spaced points 
 along an expanding closed horocycle on the modular surface. In this proble
 m\, 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 ho
 rocycle flow: Ratner’s theory does not apply. In this talk\, I will sket
 ch how this problem involves the theory of Diophantine approximation\, and
  estimates towards the Ramanujan conjecture for Hecke-Maass forms. The goa
 l is for this talk to be accessible for topologists\; no prior background 
 in analytic number theory will be assumed.\n
LOCATION:https://researchseminars.org/talk/SOQUAGAT/2/
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BEGIN:VEVENT
SUMMARY:Kathleen Petersen (Florida State University)
DTSTART:20201204T170000Z
DTEND:20201204T180000Z
DTSTAMP:20260422T225823Z
UID:SOQUAGAT/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SOQUAGAT/3/"
 >Symmetries and surface detection for $SL(2\,\\mathbb{C})$ character varie
 ties of 3-manifolds</a>\nby Kathleen Petersen (Florida State University) a
 s part of Series on open questions in Arithmetic\, Geometry and Topology\n
 \n\nAbstract\nCuller\, Morgan\, and Shalen pioneered the detection essenti
 al surfaces in 3-manifolds through $SL(2\,\\mathbb{C})$ character varietie
 s. I’ll discuss how symmetries of the 3-manifold affect this detection\,
  concluding with some examples. This is joint work with Jay Leach.\n
LOCATION:https://researchseminars.org/talk/SOQUAGAT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benson Farb (University of Chicago)
DTSTART:20201211T190000Z
DTEND:20201211T200000Z
DTSTAMP:20260422T225823Z
UID:SOQUAGAT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SOQUAGAT/4/"
 >Hilbert's 13th problem and geometry</a>\nby Benson Farb (University of Ch
 icago) as part of Series on open questions in Arithmetic\, Geometry and To
 pology\n\n\nAbstract\nHilbert's 13th Problem (H13) is a fundamental open p
 roblem about polynomials in one variable.  It is part of a beautiful (but 
 mostly forgotten) story going back 3000 years.  In this talk I will explai
 n how H13 (and related problems) fits into a wider framework that includes
  problems in enumerative algebraic geometry and the theory of modular func
 tions. I will then report on some recent progress\, joint with Mark Kisin 
 and Jesse Wolfson.\n
LOCATION:https://researchseminars.org/talk/SOQUAGAT/4/
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BEGIN:VEVENT
SUMMARY:Alan Reid (Rice University)
DTSTART:20201211T170000Z
DTEND:20201211T180000Z
DTSTAMP:20260422T225823Z
UID:SOQUAGAT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SOQUAGAT/5/"
 >Where are the arithmetic homology spheres?</a>\nby Alan Reid (Rice Univer
 sity) as part of Series on open questions in Arithmetic\, Geometry and Top
 ology\n\n\nAbstract\nIn this talk we will discuss what is known about the 
 existence of arithmetic rational homology spheres\, as well as some conjec
 tures on building others.\n
LOCATION:https://researchseminars.org/talk/SOQUAGAT/5/
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