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<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration:underline"><span style="font-size:18pt;font-family:"Times New Roman",serif">SEMINARIO
DI MATEMATICA<span></span></span></p>

<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration:underline"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span><span style="text-decoration:none"> </span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Venerdì 22 giugno 2018</span><span style="font-size:16pt;font-family:"Times New Roman",serif"><span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">ore <span>11:00</span><span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><u><span style="font-size:16pt;font-family:"Times New Roman",serif">Scuola Normale Superiore<span></span></span></u></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Pisa<span></span></span></p>

<p class="MsoNormal" align="center" style="margin:0cm 0cm 0.0001pt 9pt;text-align:center;line-height:18pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white">Aula Mancini<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><u><span style="font-size:16pt;font-family:"Times New Roman",serif"><span><span style="text-decoration:none"> </span></span></span></u></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span class="gmail-apple-converted-space"><b><span style="font-size:24pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white"> </span></b></span><span style="font-size:9.5pt;font-family:"Times New Roman",serif;color:rgb(34,34,34);background:white"> </span><b><span style="font-size:22pt;font-family:"Times New Roman",serif">Enrico Priola<span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><i><span style="font-family:"Times New Roman",serif">(Università
di Torino)</span></i><b><i><span style="font-size:22pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"><span></span></span></i></b></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><i><span style="font-family:"Times New Roman",serif;color:rgb(34,34,34)"><span> </span></span></i></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">terrà un
seminario dal titolo:<span></span></span></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" align="center" style="text-align:center;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif;color:black">“</span></b><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)">Poisson
stochastic process and basic  parabolic estimates</span></b><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif;color:black">”</span></b><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif;color:rgb(34,34,34)"><span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-size:22pt;font-family:"Times New Roman",serif"><span> </span></span></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><span lang="EN-US" style="font-family:"Times New Roman",serif">Abstract:<span></span></span></b></p>

<p class="MsoNormal" style="text-align:justify;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">We show  how  knowing Schauder  or
Sobolev-space estimates for the one-dimensional heat equation allows one to
derive their multidimensional analogs for equations with coefficients depending
only on time variable with the  same constants as in the case of the
one-dimensional heat equation. The method is   quite general and
is  based on using the Poisson stochastic process.  It also applies
to other types of  estimates and to equations involving non-local
operators.  It looks like no other methods are available at this time and
it is a  challenging problem to find an analytic approach to prove such
results.  In the talk I will concentrate on basic Sobolev estimates for the
heat equation trying to explain the method.<span></span></span></p>

<p class="MsoNormal" style="text-align:justify;background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(34,34,34)"><span> </span></span></p>

<p class="MsoNormal" style="background:white;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(34,34,34)">This is a
joint work with N. V. Krylov.<span></span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span lang="EN-US" style="font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Tutti gli interessati sono invitati a
partecipare.<span></span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif">Classe di Scienze<span></span></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><span style="font-size:16pt;font-family:"Times New Roman",serif"><span> </span></span></p>

<br clear="all"><div><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div>
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