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<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Assoc. Prof. Muhammed Uludağ<o:p></o:p></span></font></b></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;margin-bottom:
12.0pt;text-align:center'><font size=3 face=Tahoma><span style='font-size:12.0pt;
font-family:Tahoma'>(Galatasaray University)<br>
20 November Friday, at <font color=blue><span style='color:blue'>14:00</span></font>;<br>
Bilgi Üniversitesi Dolapdere Kampüsü, Room:<font color=blue><span
style='color:blue'>130.</span></font></span></font><font color=red><span
style='color:red'><o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Title: </span></font></b><o:p></o:p></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'>Modular
group, ribbons and solenoids<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'> Abstract:<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='text-align:justify;text-indent:35.4pt;text-autospace:
none'><font size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial'>I
will discuss the limit space F of the category of coverings C of the
"modular interval" as a deformation retract of the universal
arithmetic curve, which is by (my) definition nothing but the punctured
solenoid S of Penner. The space F has the advantage of being compact, unlike S.
A subcategory of C can be interpreted as ribbon graphs, supplied with an extra
structure that provides the appropriate morphisms for the category C. After a
brief discussion of the mapping class grupoid of F, and the action of the
Absolute Galois Group on F, I will turn into a certain
"hypergeometric" galois-invariant subsystem (not a subcategory) of
genus-0 coverings in C. One may define, albeit via an artificial construction,
the "hypergeometric solenoid" as the limit of the natural completion
of this subsystem to a subcategory. Each covering in the hypergeometric system
corresponds to a non-negatively curved triangulation of a punctured sphere with
flat (euclidean) triangles. The hypergeometric system is related to plane
crystallography. If time permits, I will also discuss some other natural
solenoids, defined as limits of certain galois-invariant genus-0 subcategories
of non-galois coverings in C.<o:p></o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=2 face=Arial><span
lang=EN-US style='font-size:10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
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