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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=20260403T1540&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.PZ2GUMBi.gpqA20sy@bilkent.edu.tr"
alt="" 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://sites.google.com/view/roberto-villaflor-loyola/home">Roberto
Villaflor Loyola</a></b></b></div>
<b><b><font color="#ff0000"><font color="#000000"> </font></font></b></b><b><b><font
color="#ff0000">Affiliation: </font><i>Universidad
Técnica Federico Santa María<br>
<br>
</i></b></b></div>
<div align="left"><b><b><font color="#ff0000"> Title:<font
color="#000000"> On the linear cycles
conjecture<br>
</font></font></b></b></div>
</div>
<div align="justify"><b><b><font color="#ff0000">Abstract:</font></b></b>
The classical Noether-Lefschetz theorem claims that a
very general degree d>3 surface in P3 has Picard
number one. The locus of surfaces with higher Picard
rank is known as the Noether-Lefschetz locus, which is
known to have a countable number of irreducible
components. For d>4, it is classical result due
independently to Green and Voisin, that the unique
component of highest codimension corresponds to the
locus of surfaces which contain lines. </div>
<div align="justify"><br>
</div>
<div align="justify">The natural generalization of this
question to higher dimensional hypersurfaces of the
projective space is known as the "<i>linear cycles
conjecture</i>", and remains open even for fourfolds.
For surfaces, the proof is based in the fact that
locally (analytically) one can parametrize each
component by a Hodge locus, and then use the
Infinitesimal Variation of Hodge Structure to compute
(and bound) the dimension of its Zariski tangent space.
A natural stronger version of the linear cycles
conjecture is that the Hodge loci with maximal tangent
space are those corresponding to linear cycles. </div>
<div align="justify"><br>
</div>
<div align="justify">In this talk I will report on recent
results disproving this conjecture for all degrees and
dimensions. </div>
<div align="justify"><br>
</div>
<div align="justify">This is a joint work with Jorge Duque
Franco.</div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000"><br>
</font></b></font></font></div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Date:<font
color="#000000"> 3 April 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>
<br>
</div>
<br>
<hr>
<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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