<div dir="ltr"><div style="text-align:center"><font face="times new roman, serif" size="4"><b>SEMINARIO DI ANALISI GEOMETRICA</b></font></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">

<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;text-decoration-line:underline"><span style="text-decoration-line:none"><font face="times new roman, serif" style="" size="4"><b> </b></font></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">Giovedì 8 novembre 2018</span><span style="font-size:16pt;font-family:"Times New Roman",serif"></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 14:00</span></p>

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<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></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></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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Aula Bianchi Scienze</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 style="text-decoration-line:none"> </span></span></u></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span></b></span><span style="font-size:9.5pt;font-family:Arial,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span><b><span style="font-size:22pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Giulio Tralli</span></b><b><span style="font-size:22pt;font-family:"Times New Roman",serif"></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><i><span style="font-family:"Times New Roman",serif">(<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Università di Padova</span>)</span></i></p>

<pre style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:10pt;font-family:"Courier New""><b><i><span style="font-size:12pt;font-family:"Times New Roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span></i></b></pre>

<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></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></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Hörmander operators in nondivergence form: a
Landis-type approach</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"></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:20pt;font-family:"Times New Roman",serif"> </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></b></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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">In this talk we will discuss the validity of Harnack
inequalities for</span><span lang="EN-US" style="font-family:"Times New Roman",serif"> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">linear
degenerate-elliptic equations of Hörmander type with non-smooth</span></span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">coefficients. We are interested in operators in
nondivergence form,</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">for which the
analogous of the Krylov-Safonov Harnack inequality for</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">equations with bounded measurable coefficients is
still unknown. We</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">will show a
perturbative approach to prove invariant Harnack</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">inequalities for operators with coefficients
satisfying either a</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Cordes-Landis
assumption or a continuity hypothesis. We will consider</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">two specific classes of equations: the first class is
formed by</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">degenerate-elliptic
operators which are horizontally elliptic with</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">respect to Heisenberg-type vector fields; the second
one constitutes a</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">class of
evolution operators of</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Kolmogorov-Fokker-Planck
type. This talk is mainly based on joint</span> <span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">works with F. Abedin and C.E. Gutiérrez.</span><span lang="EN-US" style="font-size:16pt;font-family:"Times New Roman",serif"></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-size:16pt;font-family:"Times New Roman",serif"> </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></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></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></p>

<div><span style="font-family:"Times New Roman",serif;font-size:16pt;text-align:justify"> </span>eria 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></div>

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