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<p class=p1><span class=s1><span lang=EN-US style='font-size:24.0pt;font-family:
Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></span></p>

<p class=p1><span class=s1><b><span lang=EN-US style='font-size:24.0pt;
font-family:Helvetica;mso-ansi-language:EN-US'>Geometry Seminar</span></b></span><b><o:p></o:p></b></p>

<p class=p2><span lang=EN-US style='mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p>

<p class=p3><span class=s1><span lang=EN-US style='font-size:11.0pt;font-family:Helvetica;mso-ansi-language:EN-US'>
	University of Tor <span class=SpellE>Vergata</span>, Department of Mathematics</span></span><span lang=EN-US style='font-size:11.0pt;
mso-ansi-language:EN-US'><o:p></o:p></span></p>









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<p class=p3><span class=s1><span lang=EN-US style='font-size:11.0pt;font-family:Helvetica;mso-ansi-language:EN-US'>
   1<sup>st</sup> of April 2025, 14:30-16:00,room <span class=SpellE>D’Antoni</span>
</span></span><span lang=EN-US style='font-size:11.0pt;mso-ansi-language:EN-US'><o:p></o:p></span></p>




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<p class=p4> &nbsp;</p>
<p class=p4>&nbsp;</p>
<p class=p3 align=left style='text-align:left'><span class=s1><b><span
style='font-family:Helvetica'><o:p>&nbsp;</o:p></span></b></span></p>
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font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>
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font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>
<p class=p3><span class=s1><b><span lang=EN-US style='font-size:11.0pt;
font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>
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<p class=p3 style="margin-left: 20%;margin-right: 20%;font-size:20.0pt;line-height: 30px"> <span class=SpellE><b> 
	Upper Bounds for the Dimensions of Brill-Noether Loci
<o:p></o:p></span></b></p>
<p class=p3><span lang=EN-US style='font-size:11.0pt;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p>




<p class=p3><span style='font-size:11.0pt'>
	Ali Bajravani
<o:p></o:p></span></p>

<p class=p3><span style='font-size:11.0pt'> 
	Humboldt Universität zu Berlin
</span><span class=s1></p>







<p class=p3><span class=s1><b><span lang=EN-US style='font-size:11.0pt;
font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>
<p class=p3><span class=s1><b><span lang=EN-US style='font-size:11.0pt;
font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>
<p class=p3><span class=s1><b><span lang=EN-US style='font-size:11.0pt;
font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>
<p class=p3><span class=s1><b><span lang=EN-US style='font-size:11.0pt;
font-family:Helvetica;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></b></span></p>



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<p class=p3><span style='font-size:11.0pt'>
	A celebrated theorem by Martens states that the dimension of the locus of line bundles of fixed degree \(d\) with at least \(k\) sections on a smooth, projective, irreducible curve of genus \(g\) doesn't exceed \(d-2k+2\). We establish similar results for various Brill-Noether loci and give some applications for higher rank Brill-Noether loci.

	
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<p class=p3><b><span style='font-size:11.0pt'><o:p>&nbsp;</o:p></span></b></p>
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This talk is part of the activity of the MIUR Excellence Department Projects <span
class=SpellE>MathMod@TOV</span>, and the PRIN 2022 Moduli Spaces and <span
class=SpellE>Birational</span> Geometry  and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures  <o:p></o:p></span></p>
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