<span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; border-collapse: collapse; "><div><p class="MsoNormal" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; ">
<span style="font-size: 20pt; font-family: Albertus; ">Mimar Sinan Güzel Sanatlar Üniversitesi</span></p></div><p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; ">
<span style="font-size: 20pt; font-family: Albertus; ">Matematik Bölümü Genel Seminerleri</span></p><p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; ">
<span style="font-size: 20pt; font-family: Albertus; "><br></span></p><p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; "><span style="font-size: 20pt; font-family: Albertus; "> <span class="Apple-style-span" style="font-family: Arial; "><span class="Apple-style-span" style="font-size: xx-large;">Additive
reducts of valued fields in positive characteristic</span></span></span></p><p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; "><span class="Apple-style-span" style="line-height: 19px; "><u><span style="line-height: 40px; "><span class="Apple-style-span" style="font-size: xx-large;"><br>
</span></span></u></span></p><p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; "><span class="Apple-style-span" style="line-height: 19px; "><u><span style="line-height: 40px; "><span class="Apple-style-span" style="font-size: xx-large;">Konuşmacı:</span></span></u></span></p>
<p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; line-height: 19px; "><span style="line-height: 40px; "><span class="Apple-style-span" style="font-size: xx-large;">Gönenç Onay</span></span></p>
<p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; line-height: 19px; "><span style="line-height: 40px; "><span class="Apple-style-span" style="font-size: xx-large;">(Universite Paris 7)</span></span></p>
<p class="MsoNormal" align="center" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; text-align: center; line-height: 19px; "><span style="line-height: 40px; "><span class="Apple-style-span" style="font-size: large;"><br>
</span></span></p><p class="MsoNormal" style="text-align: left;margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; line-height: 19px; "><span style="line-height: 40px; "><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="line-height: normal; font-size: 13px; "><span class="apple-style-span"><span style="font-family: Arial; color: black; "><span class="Apple-style-span" style="font-size: large; ">First order theories of valued fields in
characteristic $p>0$ are less explored</span></span></span><span style="font-family: Arial; color: black; "><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">then their
analogous in characteristic 0. For example, despite strong analogies</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">with field of p-adic numbers $Q_p$, we know very few
about the</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">complete theory of</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">Laurent series field $F_q((t))$. In addition, such
results can include</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">strong assumptions</span></span><span class="Apple-style-span" style="font-size: large;">
</span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">like resolution of singularities. One idea introduced
by Lou van den</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">Dries is to study</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">a such field K as a module over the ring of additive
polynomials. A</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">polynomial over $K$ is</span></span><span class="Apple-style-span" style="font-size: large;">
</span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">said to be additive if it is additive as a map on the
algebraic closure of</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">$K$. Such polynomials</span></span><span class="Apple-style-span" style="font-size: large;">
</span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">has a -<i>non commutativ</i>e- ring structure under
addition and composition.</span></span></span></span></span></span></p><p class="MsoNormal"></p><div style="text-align: left;"><span class="Apple-style-span" style="font-family: Arial; font-size: large;"><br></span></div>
<span style="font-family: Arial; color: black; "><div style="text-align: left;"><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">In this talk, after presenting motivations
arising from valued fields</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">and recalling</span></span><span class="Apple-style-span" style="font-size: large;">
</span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">some basic notions from model theory I'll will define
a class of</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">"valued modules"</span></span><span class="Apple-style-span" style="font-size: large;">
</span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">and classify all $C$-minimal such ones. Here
$C$-minimal means that</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">every definable <span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; "><span class="apple-style-span"><span style="font-family: Arial; color: black; "><span class="Apple-style-span" style="font-size: large;">1-dimensional subset is a finite Boolean
combination of balls with</span></span></span><span style="font-family: Arial; color: black; "><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">respect to valuation topology.</span></span><span class="Apple-style-span" style="font-size: large;">
</span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">As an example, $C$-minimal valued fields are
algebraically closed.</span></span><span class="Apple-style-span" style="font-size: large;"> </span></span></span></span></span></div><div style="text-align: left;"><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; "><span style="font-family: Arial; color: black; "><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><br>
</span></span></span></span></span></span></div><div style="text-align: left;"><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; "><span style="font-family: Arial; color: black; "><span class="Apple-style-span" style="font-size: large;"></span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">This talk is intended
to be</span></span><span class="Apple-style-span" style="font-size: large;"> </span><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;">accessible to students with
undergraduate algebra background.</span></span></span></span></span></span></div><div style="text-align: left;"><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; "><span style="font-family: Arial; color: black; "><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><br>
</span></span></span></span></span></span></div><div style="text-align: left;"><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; "><span style="font-family: Arial; color: black; "><span class="apple-style-span"><span class="Apple-style-span" style="font-size: large;"><span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; "><div>
<p class="MsoNormal" style="margin-top: 0px; margin-right: 21.6pt; margin-bottom: 0px; margin-left: 0px; text-align: justify; line-height: 19px; "><b><span style="font-size: 16pt; line-height: 31px; font-family: 'Arial Black'; ">Yer:</span></b><span style="font-size: 16pt; line-height: 31px; font-family: 'Arial Black'; "> 408 No’lu Amfi</span></p>
<p class="MsoNormal" style="margin-top: 0px; margin-right: 21.6pt; margin-bottom: 0px; margin-left: 0px; line-height: 19px; "><span style="font-size: 16pt; line-height: 31px; font-family: 'Arial Black'; ">MSGSÜ Fen Edebiyat Fakültesi (Beşiktaş)</span><span style="font-size: 8pt; line-height: 16px; font-family: 'Arial Black'; "></span></p>
<p class="MsoNormal" style="margin-top: 0px; margin-right: 21.6pt; margin-bottom: 0px; margin-left: 0px; line-height: 19px; "><b><span style="font-size: 16pt; line-height: 31px; font-family: 'Arial Black'; ">Zaman:</span></b><span style="font-size: 16pt; line-height: 31px; font-family: 'Arial Black'; "> <span>9 Nisan</span> 2010 Cuma, 15:00</span></p>
<div><span style="font-size: 16pt; line-height: 31px; font-family: 'Arial Black'; "><br></span></div></div></span></span></span></span></span></span></span></div></span><p></p></span>