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<p class="MsoTitle"><span style="font-family:"Times New
Roman","serif"">Colloquio
De Giorgi<o:p></o:p></span></p>
<p class="MsoTitle" style="text-align:left" align="left"><span
style="font-size:
10.0pt;font-family:"Times New
Roman","serif""><o:p><span
style="text-decoration: none"> </span></o:p></span></p>
<h2><span style="font-family:"Times New
Roman","serif";mso-no-proof:yes">Martedė
5 febbraio 2013</span><span style="font-family:"Times New
Roman","serif""><o:p></o:p></span></h2>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">ore <span
style="mso-no-proof:yes">16.00</span><o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><u><span
style="font-size:16.0pt;
font-family:"Times New Roman","serif"">Scuola
Normale Superiore<o:p></o:p></span></u></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">Pisa<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">(Sala degli
Stemmi)<o:p></o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><b><u><span
style="font-size:10.0pt;
font-family:"Times New Roman","serif""><o:p><span
style="text-decoration:none"> </span></o:p></span></u></b></p>
<p class="MsoNormal" style="text-align:center" align="center"><b
style="mso-bidi-font-weight:
normal"><span style="font-size:26.0pt;font-family:"Times
New Roman","serif"">Emmanuel
Kowalski<o:p></o:p></span></b></p>
<p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
align="center"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif"">ETH
Zuerich<o:p></o:p></span></i></p>
<p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
align="center"><i style="mso-bidi-font-style:normal"><span
style="font-size:11.0pt;font-family:
"Times New
Roman","serif";mso-no-proof:yes"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
align="center"><span
style="font-size:16.0pt;font-family:"Times New
Roman","serif"">Terrā un
seminario dal titolo:<o:p></o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><span
style="font-size:8.0pt;
font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><span style="font-size:22.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">“Trace functions over finite fields and applications”<o:p></o:p></span></b></pre>
<p class="MsoNormal" style="text-align:center" align="center"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US">Abstract:<o:p></o:p></span></i></b></p>
<pre style="text-align:justify"><i style="mso-bidi-font-style:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">In recent works with E. Fouvry and Ph. Michel, we have studied arithmetic properties of certain functions over finite fields which arise from algebraic geometry, and which contain as special cases characters and various exponential sums.<span style="mso-spacerun:yes"> </span>
The talk will explain the origin of these functions and give examples, and discuss results such as quasi-orthogonality, sums over primes of trace functions, and estimates for uniformity norms.<span style="mso-spacerun:yes"> </span>One of the main tools is the Riemann Hypothesis over finite fields.<o:p></o:p></span></i></pre>
<p class="MsoNormal" style="text-align:justify"><i
style="mso-bidi-font-style:
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<pre class="moz-signature" cols="72">--
Valeria Giuliani
Scuola Normale Superiore
Area Didattica
Servizio Supporto attivita Didattiche
tel.050509260
Fax.050509045
<a class="moz-txt-link-abbreviated" href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</a>
<a class="moz-txt-link-abbreviated" href="mailto:adi.sd@sns.it">adi.sd@sns.it</a></pre>
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