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BEGIN:VEVENT
DTSTAMP:20260225T154946Z
DTSTART:20260302T150000Z
DTEND:20260302T160000Z
SUMMARY:Manchester Geometry Seminar - Lasse Rempe
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}s1q3-mm27n1
 ex-urw2t3
DESCRIPTION:Speaker: Lasse Rempe (Manchester)\n\nAbstract. In 1965\, cart
 ographer L. P. Lee proposed using a conformal map of a tetrahedron to th
 e sphere as the basis for a map projection with less dramatic area disto
 rtion than the classical projections. While this has not caught on\, it 
 suggests the following mathematical question: Which orientable surfaces 
 can be conformally represented on a collection of equilateral triangles?
  Equivalently\, which such surfaces can be built (up to a conformal chan
 ge of coordinate) by glueing together a finite or infinite collection of
  copies of a closed equilateral triangle? Such surfaces are called *equi
 laterally triangulable*. \n\nThe answer in the compact case is given by 
 a famous classical theorem of Belyi\, which states that a compact Rieman
 n surface is equilaterally triangulable if and only if it is defined ove
 r a number field. These *Belyi surfaces* - and their associated “dessins
  d’enfants” - have found applications across many fields of mathematics\
 , including mathematical physics.\n\nIn joint work with Chris Bishop\, w
 e give a complete answer of the same question for the case of infinitely
  many triangles (i.e.\, for non-compact Riemann surfaces). In some sense
 \, the talk follows on from my inaugural lecture last year\, but attendi
 ng that lecture is not a pre-requisite for attending the seminar talk\, 
 which should be accessible to a wide audience including postgraduate stu
 dents. In the first half of the talk\, I will summarise and review the m
 ain results\, while in the second half I will discuss some of the ideas 
 and techniques that go into the proof\, including elementary constructio
 ns of "almost" equilateral triangulations\, as well as results from the 
 theory of quasiconformal mappings and Teichmüller theory.\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room 1\, Alan Turing Building\, Manchester
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