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SUMMARY:Philipp Bader (University of Glasgow)
DTSTART:20251211T133000Z
DTEND:20251211T143000Z
DTSTAMP:20260423T021040Z
UID:GaTO/127
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/127/">T
 eichmüller curves via the Hurwitz-Hecke construction</a>\nby Philipp Bade
 r (University of Glasgow) as part of Geometry and topology online\n\nLectu
 re held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nA
 bstract\nTeichmüller curves are totally geodesic algebraic curves inside 
 the moduli space of Riemann surfaces of genus $g$. There are fascinating c
 onnections between Teichmüller curves and billiard flows on polygons.\n\n
 Given a Teichmüller curve\, there is a way to construct another\, in high
 er genus\, by taking a branched cover. If a Teichmüller curve does not ar
 ise in this way\, we call it <i>primitive</i>. The classification of primi
 tive Teichmüller curves is a problem that has been widely explored in the
  past decades but still leaves many questions unanswered. In fact\, only i
 n genus two there exists a complete classification. In every genus startin
 g from five and higher only finitely many examples of primitive Teichmüll
 er curves have been found.\n\nIn this talk\, we introduce the notions desc
 ribed above and present the so-called Hurwitz-Hecke construction\; a metho
 d that can be used to construct Teichmüller curves. We will see that this
  construction gives rise to many of the known examples of Teichmüller cur
 ves. \n\nThis is joint work in progress with Paul Apisa and Luke Jeffreys.
 \n
LOCATION:https://researchseminars.org/talk/GaTO/127/
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