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<div align="center"><big><b><big>Welcome to the 2026
Spring talks of ODTÜ-Bilkent Algebraic Geometry
Seminars</big></b></big><b><br>
</b></div>
<div align="center"><i>since 2000</i><br>
</div>
<div align="center"><b><b>=================================================================</b></b><br>
<br>
This week the <a
href="http://www.bilkent.edu.tr/~sertoz/agseminar.htm"
target="_blank" moz-do-not-send="true">ODTÜ-Bilkent
Algebraic Geometry Seminar</a> is <b>online</b><br>
<br>
<i><font color="#ff00ff">This talk will begin at <u><b>15:40</b></u><u> (GMT+3)</u></font></i><br>
<a
href="https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20260313T1540&p1=19&ah=1"
target="_blank" moz-do-not-send="true">Please check
your time difference between Ankara and your city here</a><br>
<b>=================================================================<br>
<br>
</b></div>
<div align="center">
<div align="center"><img
src="cid:part1.ckRwWkSZ.dhb9Usyp@bilkent.edu.tr"
alt="" width="522" height="583" class=""></div>
</div>
<div align="center"><br>
</div>
<div align="center"><i>Ben Viegers (1886-1947)<br>
</i></div>
<div align="center"><i><br>
</i></div>
<div align="center"><i><br>
</i>
<div align="left">
<div align="left"><b><b moz-do-not-send="true"
href="https://fens.sabanciuniv.edu/tr/faculty-members/detail/3419"><font
color="#ff0000">Speaker: </font> <a
moz-do-not-send="true"
href="https://math.univ-cotedazur.fr/%7Emancona/">Michele Ancona</a></b></b></div>
<b><b><font color="#ff0000"><font color="#000000"> </font></font></b></b><b><b><font
color="#ff0000">Affiliation: </font><i>Université
Côte d'Azur<br>
<br>
</i></b></b></div>
<div align="left"><b><b><font color="#ff0000"> Title:<font
color="#000000"> Harnack manifolds<br>
</font></font></b></b></div>
</div>
<div align="justify"><b><b><font color="#ff0000">Abstract:</font></b></b>
Abstract: In 1876, Axel Harnack proved in a
foundational article that<br>
<br>
1) every real algebraic curve of degree d in RP^2 has at
most (d-1)(d-2)/2 + 1 connected components;<br>
2) for every d there exists a curve of degree d with
exactly this number of connected components.<br>
<br>
Over the past 150 years, these results have played a
central role in the study of the topology of real
algebraic varieties. The first part of Harnack’s theorem
generalizes to the so-called Smith–Floyd inequality for
arbitrary real algebraic varieties: the sum of the Betti
numbers of the real part is at most the corresponding
sum for the complex part. Despite spectacular advances,
the generalization of the second part of Harnack’s
theorem remains open in the case of projective
hypersurfaces.<br>
<br>
For these, however, Ilia Itenberg and Oleg Viro showed
that the Smith–Floyd inequality is asymptotically
optimal by using the combinatorial patchworking
technique. In joint work with Erwan Brugallé and
Jean-Yves Welschinger, we show that an elementary
generalization of Harnack’s original construction method
in dimension 2 yields this asymptotic optimality for any
ample line bundle on a real algebraic variety. Beyond
Betti numbers, we also describe the diffeomorphism type
of an open subset of these topologically rich varieties.</div>
<div align="justify"><br>
</div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Date:<font
color="#000000"> 13 March 2026, Friday</font></font></b></font></font></div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Time: </font>15:40 <i>(GMT+3)</i></b><br>
<b><font color="#ff0000">Place: </font></b><font
color="#ff0000"><font color="#000000"><b>Zoom</b></font></font></font></font></div>
<blockquote>
<p><i><b>Participants who have registered will receive
the Zoom link via email one day before the
seminar.</b></i></p>
<p><i><b>If you registered for a previous talk in this
series, there's no need to register again—you'll
automatically receive the link for this session.</b></i></p>
<p><i><b moz-do-not-send="true"
href="mailto:sertoz@bilkent.edu.tr">If you haven't
registered yet, please contact <a
href="mailto:sertoz@bilkent.edu.tr"
class="moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
to be added to the mailing list.</b></i></p>
</blockquote>
<div align="left">You are most cordially invited to
attend.</div>
<div align="left"><br>
</div>
<div align="left">Ali Sinan Sertöz</div>
<div align="left"><br>
</div>
<div align="center">
<div align="center"><b><font color="#0080c0"><i><b><font
color="#0080c0"><i>This seminar series is
organized by a joint team from ODTÜ and
Bilkent<br>
<br>
Alexander Degtyarev (Bilkent)<br>
Ali Sinan Sertöz (Bilkent) contact person<br>
Ali Ulaş Özgür Kişisel (ODTÜ)<br>
Yıldıray Ozan (ODTÜ)<br>
</i></font></b></i></font></b></div>
<div align="left"><br>
</div>
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<pre cols="72">----------------------------------------------------------------------------
Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
e-mail: <a href="mailto:sertoz@bilkent.edu.tr" target="_blank"
class="gmail-moz-txt-link-freetext moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
Web: <a href="http://sertoz.bilkent.edu.tr" target="_blank"
moz-do-not-send="true">sertoz.bilkent.edu.tr</a>
----------------------------------------------------------------------------</pre>
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