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<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Tarih (Date) :</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> 25.10.2015, Çarşamba
(</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Wednesday</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">)<span style="mso-spacerun:yes">                    </span></span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Saat (Time):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> 15:00</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Yer (Place):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> Yaşar ATAMAN Seminer
Salonu</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span></p>

<p class="MsoNormal" style="margin-bottom:12pt;line-height:normal"><b style="mso-bidi-font-weight:
normal"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Konuşmacı (Speaker):</span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white none repeat scroll 0% 0%">Y. Doç. Dr. İbrahim Ünal (ODTÜ)</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Başlık (Title): </span></b><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Calibrated Geometries
and φ-free Submanifolds</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"> </span></b></p>

<p class="MsoNormal"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;line-height:115%;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Özet (Abstract) : </span></b><span style="font-size:14pt;line-height:115%;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Calibrated geometries, introduced by
Harvey and Lawson in 1982, are the geometries of calibrated submanifolds, a
distinguished type of minimal submanifolds determined by a fixed, closed
differential form φ called a calibration on a Riemannian manifold <i style="mso-bidi-font-style:normal">M</i>. A Kahler form ω in complex geometry
provides the first rich example of a calibration and calibrated geometries can
be viewed as the generalization of Kahler manifolds as they have many similar
properties. Recently, the introduction of plurisubharmonic functions on
calibrated manifolds, which provides us doing analysis on them very similar to
the one on complex manifolds, has made another type of submanifolds very
important. These submanifolds are called as φ-free and are the generalization
of totally real submanifolds of complex manifolds.</span></p>

<p class="MsoNormal"><span style="font-size:14pt;line-height:115%;font-family:"Times New Roman",serif;color:rgb(34,34,34)">In this talk, I will start with an introduction to
calibrated manifolds, and give the most well-known examples coming from special
holonomy. Then, I will talk about the geometry and topology of φ-free submanifolds.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">NOT: Konuşma sonunda çay ve pasta ikramı olacaktır.</span></p>

<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal;background:white none repeat scroll 0% 0%"><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">(P.S.<span style="mso-spacerun:yes">  </span>Tea and </span><span style="font-size:14pt;font-family:"Times New Roman",serif">cookies will be
served after the talk</span><span style="font-size:14pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">.)</span></p>

<div><div class="gmail_signature"><div dir="ltr">  <br><br>  Mesut Sahin<div>  Associate Professor<br>  Department of Mathematics<br>  Hacettepe University<br>  TR 06800 Beytepe </div><div>  ANKARA - TURKEY<br> <a href="http://yunus.hacettepe.edu.tr/~mesut.sahin" target="_blank">http://yunus.hacettepe.edu.tr/~mesut.sahin</a></div></div></div></div>
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