<div dir="ltr"><div class="gmail_default" style="font-family:verdana,sans-serif"><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"><b><span style="font-size:16pt;font-family:'Times New Roman',serif">martedì 10 maggio 2016</span></b><b><span style="font-size:16pt;font-family:'Times New Roman',serif"></span></b></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 15:00</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 Tonelli</span></p>
<p class="MsoNormal"><b><u><span style="font-size:10pt;font-family:'Times New Roman',serif"><span style="text-decoration:none"> </span></span></u></b></p>
<p class="MsoNormal" align="center" style="text-align:center"><b><i><span style="font-size:26pt;font-family:'Times New Roman',serif">Cheng Jih-Hsin</span></i></b></p>
<p class="MsoNormal" align="center" style="text-align:center"><i><span style="font-family:'Times New Roman',serif">Academia
Sinica</span></i><i><span style="font-family:'Times New Roman',serif"></span></i></p>
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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><i><span lang="EN-GB" style="font-size:28pt;font-family:'Times New Roman',serif">“</span></i></b><b><span lang="EN-GB" style="font-size:28pt;font-family:'Times New Roman',serif">A local index theorem for CR manifolds with $S^1$
action</span></b><b><i><span lang="EN-GB" style="font-size:28pt;font-family:'Times New Roman',serif">”</span></i></b><b><span lang="EN-GB" style="font-size:28pt;font-family:'Times New Roman',serif"></span></b></p>
<p class="MsoNormal" style="text-align:justify"><b><i><span lang="EN-GB" style="font-size:10pt;font-family:'Times New Roman',serif"> </span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><b><i><span lang="EN-GB" style="font-size:10pt;font-family:'Times New Roman',serif"> </span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><b><i><span lang="EN-GB" style="font-size:10pt;font-family:'Times New Roman',serif">Abstract:</span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><i><span lang="EN-GB" style="font-family:'Times New Roman',serif">Among those transversally elliptic
operators initiated by Atiyah and Singer, Kohn's $\Box_b$ operator on CR
manifolds with $S^1$ action is a natural one of geometric significance for
complex analysts. Our main result computes a local index density, in terms of
\emph{tangential} characteristic forms, on such manifolds including
\emph{Sasakian manifolds} of interest in String Theory. As applications of our
CR index theorem we can prove a CR version of Grauert-Riemenschneider
criterion, and produce many CR functions on a weakly pseudoconvex CR manifold
with transversal $S^1$ action and many CR sections on some class of CR
manifolds, answering some long-standing questions raised by Kohn and Henkin
respectively. Moreover in some cases, we can reinterpret Kawasaki's Hirzebruch-Riemann-Roch
formula for a complex orbifold with an orbifold holomorphic line bundle as an
index theorem obtained by an integral over a smooth CR manifold which is
essentially the circle bundle of this line bundle. This is joint work with
Chin-Yu Hsiao and I-Hsun Tsai</span></i><b><i><span lang="EN-GB" style="font-size:10pt;font-family:'Times New Roman',serif"></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><span lang="EN-GB" style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>
<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=""><span style="font-size:16pt;font-family:'Times New Roman',serif"> Classe
di Scienze</span></p>
<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif"> Matematiche
e Naturali</span></p></div><div><br></div>-- <br><div class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><span style="color:rgb(84,141,212);font-family:Cambria,serif;font-size:9pt"><br></span></div><div dir="ltr"><span style="color:rgb(84,141,212);font-family:Cambria,serif;font-size:9pt">- - - - -</span><br></div><div dir="ltr"><p><span style="font-size:9pt;font-family:Cambria,serif;color:rgb(84,141,212)">
Michele VERDE<br>
Scuola Normale Superiore</span></p>
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