<div dir="ltr"><p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration-line:underline"><span style="font-size:18pt;font-family:"Times New Roman",serif">SEMINARIO
DI MATEMATICA</span></p>

<p class="gmail-MsoTitle" style="margin:0cm 0cm 0.0001pt;text-align:center;font-size:24pt;font-family:"New York",serif;font-weight:bold;text-decoration-line:underline"><span style="font-size:10pt;font-family:"Times New Roman",serif"><span style="text-decoration-line:none"> </span></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"><b><span style="font-size:16pt;font-family:"Times New Roman",serif">Martedì 27 novembre 2018</span></b><b><span style="font-size:16pt;font-family:"Times New Roman",serif"></span></b></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 11:00</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"> </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"><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">Aula Bianchi Scienze</span></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><u><span style="font-size:22pt;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"><b><span style="font-size:22pt;font-family:"Times New Roman",serif">Marcus Carlsson</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"><span style="font-family:"Times New Roman",serif">(Lund University)</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"><span style="font-family:"Times New Roman",serif"> </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">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-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><i><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif">“</span></i></b><b><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif;color:rgb(33,33,33)"> Perturbation theory for the
spectral decomposition of matrices</span></b><b><i><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif">”</span></i></b><b><span lang="EN-US" style="font-size:20pt;font-family:"Times New Roman",serif;color:rgb(33,33,33)"></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><i><span lang="EN-US" style="font-size:10pt;font-family:"Times New Roman",serif"> </span></i></b></p>

<p class="MsoNormal" align="center" style="text-align:center;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><i><span lang="EN-US" style="font-size:10pt;font-family:"Times New Roman",serif"> </span></i></b></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><i><span lang="EN-US" style="font-size:11pt;font-family:"Times New Roman",serif">Abstract:</span></i></b></p>

<p class="MsoNormal" style="text-align:justify;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 lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(33,33,33)">Consider a Hermitian matrix and a small perturbation.
We will consider how the eigenvalues and eigenvectors change with the
perturbation. Typical theorems concerning this either consider a perturbation
along a line or provide general estimates valid for all perturbations (such as
Weyl’s inequalities). We first give an overview of the field and then
provide new results which are global in the sense that the perturbation is not
restricted to a line, but local in the sense that the estimates are valid
modulo certain ordo terms.</span></p>

<p class="MsoNormal" style="text-align:justify;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 lang="EN-US" style="font-family:"Times New Roman",serif;color:rgb(33,33,33)">We apply this to the functional calculus of the matrix
square root and matrix modulus. In the kernel-free case the corresponding
result follows from the so called Daleskii-Krein theorem.</span></p>

<p class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-p1" style="margin:0cm 0cm 0.0001pt;text-align:justify;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:12pt;font-family:"Times New Roman",serif"><span class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-s1"><span lang="EN-US" style="color:rgb(50,51,51)"> </span></span></p>

<p class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-p1" style="margin:0cm 0cm 0.0001pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:12pt;font-family:"Times New Roman",serif"><span class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-s1"><span style="font-size:16pt;color:rgb(50,51,51)">Tutti gli interessati sono invitati a partecipare.</span></span></p>

<p class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-p1" style="margin:0cm 0cm 0.0001pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:12pt;font-family:"Times New Roman",serif"><span class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-s1"><span style="font-size:16pt;color:rgb(50,51,51)"> </span></span></p>

<p class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-p1" style="margin:0cm 0cm 0.0001pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:12pt;font-family:"Times New Roman",serif"><span class="gmail-m-574669422465302732gmail-m-3576957482508322898gmail-s1"><span style="font-size:16pt;color:rgb(50,51,51)">Classe di Scienze</span></span><span style="font-size:16pt;color:rgb(50,51,51)"></span></p>

<p class="MsoNormal" style="text-align:justify;margin:0cm 0cm 0.0001pt;font-size:12pt;font-family:TradeGothicPl-CondEighteen"><b><i><span style="font-family:"Times New Roman",serif"> </span></i></b></p><div><div dir="ltr" class="gmail_signature" data-smartmail="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></div>

<p></p>

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