<div dir="ltr"><p class="" style="text-align:center"><span style="font-size:22pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">Seminario di Matematica</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">Lunedì 16 novembre 2015</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>

<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">Aula Bianchi Scienze</span></p>

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<pre style="text-align:center"><b><span style="font-size:22pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">Chinh Lu</span></b></pre><pre style="text-align:center"><i><span style="font-size:12pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">( Centro De Giorgi)</span></i></pre>

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<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" align="center" style="text-align:center"><b><span lang="EN-US" style="font-size:22pt;font-family:'Times New Roman',serif">“<span class=""><span style="background-image:initial;background-repeat:initial"> </span></span><span style="background-image:initial;background-repeat:initial">Convexity of the extended Mabuchi energy
and the large time behaviour of the weak Calabi flow</span>”</span></b></p>

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<p class="MsoNormal"><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"><i><span lang="EN-US" style="background-image:initial;background-repeat:initial">Let X be  a
compact Kahler manifold. In this talk we first establish the convexity of the
Mabuchi energy along finite energy geodesics in the competion of the space of
Kahler metrics (the case of C^1,1 geodesics was proved by Berman-Berndtsson).
Secondly,  following the program of J. Streets we use this to study
the  asymptotics of the weak  Calabi flow which is  the gradient
flow of the  Mabuchi energy in the CAT(0) space of Kahler metrics. This
flow exists for all times and coincide with the smooth one whenever the latter
exists. We show that it either diverges or it converges, in the 
pluripotential sense,  to some minimiser of the functional. This gives the
first concrete result about the long time convergence of this flow on general
Kahler manifolds, partially confirming a conjecture of Donaldson.  This is
joint work with Robert Berman and Tamas Darvas<span class=""> </span></span></i><i><a href="http://arxiv.org/abs/1510.01260" target="_blank" style="text-align:start"><span lang="EN-US" style="background-image:initial;background-repeat:initial">http://arxiv.org/abs/1510.01260</span></a></i><i><span lang="EN-US" style="background-image:initial;background-repeat:initial"><span style="text-align:start">.</span></span></i><b><i><span lang="EN-US"></span></i></b></font></p>

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

<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>

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

<p class=""><span style="font-size:16pt;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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