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<div align="center"><big> <b><big><br>
</big></b></big></div>
<div align="center"><big><b><big>Welcome to the 2021 Fall talks
of ODTU-Bilkent Algebraic Geometry Seminars</big></b></big><b><br>
</b><b> </b><b> </b></div>
<b> </b>
<div align="center"><i>since 2000</i><br>
<b> </b> </div>
<div align="center"><b> </b><b> </b><b><b>=================================================================</b>
</b><br>
<b> </b><br>
This week the <a
href="http://www.bilkent.edu.tr/%7Esertoz/agseminar.htm"
target="_blank" moz-do-not-send="true">ODTU-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>
<br>
<b>=================================================================</b></div>
<div align="center"><br>
<br>
<div align="center"><b><img
src="cid:part1.xQvoIsn0.9FNpOac3@bilkent.edu.tr" alt=""
class="" width="498" height="391"> </b><font size="-1"><i>
</i></font></div>
<div align="center"><font size="-1"><i>Paul Gauguin
(1848-1903)<br>
</i></font></div>
<div align="left"><br>
<b><b><font color="#ff0000">Speaker:<font color="#000000">
Alexander Degtyarev<br>
</font></font></b></b></div>
<div align="left"><b><b><font color="#ff0000">Affiliation: <font
color="#000000">Bilkent</font><br>
Title:<font color="#000000"> Conics on polarized
K3-surfaces<br>
</font><br>
</font></b></b></div>
</div>
<div align="left"><b><b><font color="#ff0000">Abstract:</font></b></b><font
color="#ff0000"><font color="#000000"> Generalizing Barth
and Bauer, denote by N_2n(d) the maximal number of smooth
degree d rational curves that can lie on a smooth
2n-polarized K3-surface X⊂Pn. Originally, the question was
raised in conjunction with smooth spatial quartics, which
are K3-surfaces.<br>
<br>
The numbers N_2n(1) are well understood, whereas the only
known value for d=2 is N_6(2)=285. I will discuss my
recent discoveries that support the following conjecture
on the conic counts in the remaining interesting degrees.<br>
<br>
Conjecture. One has N_2(2)=8910, N_4(2)=800, and
N_8(2)=176.<br>
<br>
The approach used does not distinguish (till the very last
moment) between reducible and irreducible conics. However,
extensive experimental evidence suggests that all conics
are irreducible whenever their number is large enough.<br>
<br>
Conjecture. There exists a bound N∗_2n(2)<N_2n(2) such
that, whenever a smooth 2n-polarized K3-surface X has more
than N∗_2n(2) conics, it has no lines and, in particular,
all conics on X are irreducible.<br>
<br>
We know that 249≤N∗_6(2)≤260 is indeed well defined, and
it seems feasible that N∗_2(2)≥8100 and N∗_4(2)≥720 are
also defined; furthermore, conjecturally, the lower bounds
above are the exact values.<br>
<br>
</font></font></div>
<div align="left"><font color="#ff0000"><font color="#000000"><b><font
color="#ff0000">Date:<font color="#000000"> 26
November 2021</font></font></b>, Friday</font></font><br>
</div>
<div align="left"><font color="#ff0000"><font color="#000000"><b>
<font color="#ff0000">Time: </font>15:40</b><br>
<b><font color="#ff0000">Place: </font></b><font
color="#ff0000"><font color="#000000"><b>Zoom<br>
</b></font></font></font></font></div>
<div align="left"><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><br>
</b></font></font></font></font></div>
<blockquote>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">One
day before the seminar, an announcement with the
Zoom meeting link will be sent to those who
registered with Sertöz. <br>
</b></b></font></font></font></font></p>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">If
you have registered before for one of the
previous talks, there is no need to register
again; you will automatically receive a link for
this talk too.<br>
</b></b></font></font></font></font></p>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">If
you have not registered before, please contact
him at <a
href="mailto:sertoz@bilkent.edu.tr?subject=Zoom%20Seminar%20Address%20Request"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>.</b></b></font></font></font></font></p>
</blockquote>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b> </b></font></font></font></font></p>
<div align="left"><br>
</div>
<div align="left">Please bring your own tea and cookies and
self-serve at the convenience of your own home! 😁<span
class="gmail-moz-smiley-s1"></span></div>
<div align="left"><br>
</div>
<div align="left">You are most cordially invited to attend.</div>
<div align="left"><br>
</div>
<div align="left">Ali Sinan Sertöz<br>
<font color="#ff0000"><font color="#000000"><b><font
color="#ff0000"> </font></b></font></font></div>
<pre class="gmail-moz-signature" cols="72">----------------------------------------------------------------------------
Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Turkey
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
Fax: (90)-(312) - 290 1797
e-mail: <a class="gmail-moz-txt-link-abbreviated moz-txt-link-freetext" href="mailto:sertoz@bilkent.edu.tr" moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
Web: <a href="http://sertoz.bilkent.edu.tr" moz-do-not-send="true">sertoz.bilkent.edu.tr</a>
----------------------------------------------------------------------------</pre>
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