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</o:shapelayout></xml><![endif]--></head><body lang=IT link=blue vlink=purple><div class=WordSection1><p class=MsoTitle><span style='font-size:18.0pt;font-family:"Times New Roman","serif"'>SEMINARIO MATEMATICA<o:p></o:p></span></p><p class=MsoTitle><span style='font-size:10.0pt;font-family:"Times New Roman","serif"'><o:p><span style='text-decoration:none'> </span></o:p></span></p><h2><span style='font-family:"Times New Roman","serif"'>giovedì 17 luglio 2014</span><o:p></o:p></h2><p class=MsoNormal align=center style='margin-left:9.0pt;text-align:center;line-height:18.0pt'><span style='font-size:18.0pt;font-family:"Times New Roman","serif"'>ore <b>10:00 <o:p></o:p></b></span></p><p class=MsoNormal align=center style='margin-left:9.0pt;text-align:center;line-height:18.0pt'><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></p><p class=MsoNormal align=center style='margin-left:9.0pt;text-align:center;line-height:18.0pt'><u><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'>Scuola Normale Superiore<o:p></o:p></span></u></p><p class=MsoNormal align=center style='margin-left:9.0pt;text-align:center;line-height:18.0pt'><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'>Pisa<o:p></o:p></span></p><p class=MsoNormal align=center style='margin-left:9.0pt;text-align:center;line-height:18.0pt'><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'>Aula Mancini<o:p></o:p></span></p><p class=MsoNormal><b><u><span style='font-size:10.0pt;font-family:"Times New Roman","serif"'><o:p><span style='text-decoration:none'> </span></o:p></span></u></b></p><p class=MsoNormal align=center style='text-align:center'><b><i><span style='font-size:26.0pt;font-family:"Times New Roman","serif"'>Marco Abate<o:p></o:p></span></i></b></p><p class=MsoNormal align=center style='text-align:center'><i><span style='font-family:"Times New Roman","serif"'>Dipartimento di Matematica, Pisa</span></i><i><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p></o:p></span></i></p><p class=MsoNormal align=center style='text-align:center'><span style='font-family:"Times New Roman","serif"'><o:p> </o:p></span></p><p class=MsoNormal align=center style='text-align:center'><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'>Terrà un seminario dal titolo:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></p><p class=MsoNormal align=center style='text-align:center'><b><i><span lang=EN-US style='font-size:28.0pt;font-family:"Times New Roman","serif"'>“</span></i></b><b><span lang=EN-US style='font-size:28.0pt;font-family:"Times New Roman","serif"'>Geodesic flow and index theorems for meromorphic connections</span></b><b><i><span lang=EN-US style='font-size:28.0pt;font-family:"Times New Roman","serif"'>”</span></i></b><b><span lang=EN-US style='font-size:28.0pt;font-family:"Times New Roman","serif"'><o:p></o:p></span></b></p><p class=MsoNormal style='text-align:justify'><b><i><span lang=EN-US style='font-size:10.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></i></b></p><p class=MsoNormal style='text-align:justify'><b><i><span lang=EN-US style='font-size:10.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></i></b></p><p class=MsoNormal style='text-align:justify'><b><i><span lang=EN-US style='font-size:10.0pt;font-family:"Times New Roman","serif"'>Abstract:<o:p></o:p></span></i></b></p><p class=MsoNormal style='text-align:justify'><i><span lang=EN-US style='font-family:"Times New Roman","serif"'>The study of meromorphic connections on Riemann surfaces is a classical topic, related for instance to the 21st Hilbert problem.</span></i><i><span lang=EN-US style='font-size:12.0pt;font-family:"Times New Roman","serif"'><o:p></o:p></span></i></p><p class=MsoNormal style='text-align:justify'><i><span lang=EN-US style='font-family:"Times New Roman","serif"'>In this talk I shall introduce a novel point of view, with unexpected analytic, geometric and dynamical applications. More precisely, I shall show how to associate to holomorphic maps having a positive-dimensional fixed point set a meromorphic connection along a foliation in Riemann surfaces, that can be used to prove several index theorems generalizing and extending both the classical holomorphic Lefschetz index theorem and the Baum-Bott and Camacho-Sad index theorems for foliations. Furthermore, I shall describe how to study with analytical and geometrical techniques the geodesic flow associated to a meromorphic connection, with the aim of describing the asymptotic behavior of the real geodesic defined by the connection. Finally, I shall describe a few applications of these results to the study of the dynamics of germs tangent to the identity, to the study of the flow of homogeneous vector fields, and to the study of meromorphic self-maps of the complex projective space.</span></i><b><i><span lang=EN-US style='font-size:10.0pt;font-family:"Times New Roman","serif"'><o:p></o:p></span></i></b></p><p class=MsoNormal style='text-align:justify'><span lang=EN-US style='font-size:16.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></p><p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'>Tutti gli interessati sono invitati a partecipare.<o:p></o:p></span></p><p class=Corpodeltesto><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'><o:p> </o:p></span></p><p class=Corpodeltesto><span style='font-size:16.0pt;font-family:"Times New Roman","serif"'> Classe di Scienze<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Georgia","serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Georgia","serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'>- - - - -<br>Michele VERDE<br>Scuola Normale Superiore<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'>Servizio alla didattica e allievi<br>Piazza Dei Cavalieri, 7<br>I - 56126 Pisa<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'>Tel. 050-509048<br>E-Mail: </span><a href="mailto:michele.verde@sns.it"><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'>michele.verde@sns.it</span></a><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'><br>E-Mail: </span><a href="mailto:classi@sns.it"><span style='font-size:9.0pt;font-family:"Cambria","serif";color:blue;mso-fareast-language:IT'>classi@sns.it</span></a><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'><br>- - - - -<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Cambria","serif";color:#548DD4;mso-fareast-language:IT'>Le informazioni contenute nella presente e-mail e nei relativi allegati possono essere riservate e sono, comunque, destinate esclusivamente al destinatario in indirizzo.<br>E’ vietata, pertanto, la diffusione, distribuzione e/o copiatura di tali informazioni da parte di qualsiasi soggetto diverso dal destinatario. <br>Chiunque abbia ricevuto o letto questa e-mail per errore o senza esserne legittimato è invitato a darne immediatamente notizia al mittente tramite fax o e-mail e a distruggerla.<br>Grazie.<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>