<div dir="ltr"><p class="" style="text-align:center"><span style="font-size:18pt;font-family:'Times New Roman',serif">SEMINARIO
DI MATEMATICA</span></p>

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<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Mercoledì 6 aprile 2016</span><span style="font-size:16pt;font-family:'Times New Roman',serif"></span></p>

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

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<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-repeat:initial"><b><span style="font-size:22pt;font-family:'Times New Roman',serif">Luciano Mari</span></b></p>

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<pre style="text-align:center"><b><i><span style="font-size:12pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial"> </span></i></b></pre>

<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:'Times New Roman',serif">terrà un
seminario dal titolo:</span></p>

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<p class="MsoNormal" style="text-align:center;background-image:initial;background-repeat:initial"><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">The
Ahlfors-Khas’minskii duality for fully nonlinear PDEs, and geometric
applications<span style="color:black">”</span></span></b></p>

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<p class="MsoNormal" style="text-align:justify"><b><span lang="EN-US" style="font-family:'Times New Roman',serif">Abstract:</span></b></p>

<p class="MsoNormal" style="text-align:justify"><font face="arial, helvetica, sans-serif"><span lang="EN-US">Maximum
principles at infinity (or ”almost maximum principles”) are a powerful tool to
investigate the geometry of Riemannian manifolds. Among them, we stress the
Ekeland, the Omori-Yau principles and their weak versions, in the sense of
Pigola-Rigoli-Setti. These last have nice probabilistic counterparts in terms
of stochastic and martingale completeness, which in turn are related to
potential theory and parabolicity. The validity of such principles is usually
granted via suitable exhaustion functions called Evans-Khas’minskii potentials.
In this talk, I discuss an underlying, unifying duality that allows to uncover
relations between the principles. Indeed, duality holds for a broad class of
fully-nonlinear operators of geometric interest. Our methods use the approach
to nonlinear PDEs pioneered by Krylov (’95) and Harvey-Lawson (’09 - ), and
involve the study of viscosity “almost solutions” of obstacle type problems. </span>This is joint work with Leandro
F. Pessoa. </font><font face="Times New Roman, serif"></font></p>

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

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<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:'Times New Roman',serif">Classe di Scienze Matematiche e Naturali</span></p>

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<p class=""><span style="font-size:18pt;font-family:'Times New Roman',serif"> </span></p><div><div class="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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