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<p class="MsoNormal"><span lang="EN-US">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">This is happening today. Fun with analysis and topology. I hope to see you there!<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;color:black">From: </span></b><span style="font-size:12.0pt;color:black">Federica Pasquotto <f.pasquotto@math.leidenuniv.nl><br>
<b>Date: </b>Thursday, 13 April 2023 at 13:28<br>
<b>To: </b>Federica Pasquotto <f.pasquotto@math.leidenuniv.nl><br>
<b>Subject: </b>DDT&G seminar tomorrow in Amsterdam: Niels Waterstraat<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">Dear all,</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span style="font-size:12.0pt;color:black">This is to remind you that<span class="xcontentpasted0"> Niels Waterstraat (MLU Halle-Wittenberg) will speak in the </span><span class="mark4fg7cf1ms">DDT&G</span><span class="xcontentpasted0"> seminar
tomorrow (Friday) afternoon. </span><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">The title of his minicourse will be </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
<p class="xxelementtoproof" align="center" style="text-align:center;background:white">
<span class="xxxcontentpasted0"><i><span style="font-size:12.0pt;color:black">"Spaces of Self-adjoint Fredholm Operators and the Spectral Flow" </span></i></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">(see below for the abstract). </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">We will start at
<b>14:00</b> in room <b>9-A46</b> (NU building, Amsterdam).</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">It will also be possible to attend remotely using the login details below:</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white;text-align:start"><span style="color:#242424"><o:p> </o:p></span></p>
<p style="background:white;text-align:start"><span class="contentpasted3"><span style="font-size:12.0pt;color:black">https://us06web.zoom.us/j/85884234839</span></span><span style="color:#242424"><o:p></o:p></span></p>
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<p style="background:white"><span class="contentpasted3"><span style="font-size:12.0pt;color:black">Meeting ID: 858 8423 4839</span></span><span style="color:#242424"><o:p></o:p></span></p>
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<p style="background:white;text-align:start"><span class="contentpasted3"><span style="font-size:12.0pt;color:black">Passcode: 304030</span></span><span style="color:#242424"><o:p></o:p></span></p>
<p class="xxelementtoproof" style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="xxelementtoproof" style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">We hope to see many of you tomorrow!</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black">Alvaro, Federica, and Thomas.</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="xxxcontentpasted0"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><b><span style="font-size:12.0pt;color:black">Abstract:</span></b><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="background:white"><span class="contentpasted2"><span style="font-size:12.0pt;color:black">The spectral flow is an integer-valued homotopy invariant for paths of self-adjoint Fredholm operators that was invented by Atiyah, Patodi
and Singer in the seventies, for investigating elliptic differential operators on manifolds. Later it was used by Floer in the construction of his famous homology groups and became a well-known invariant in global and symplectic analysis as well as mathematical
physics in the decades since. </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span class="contentpasted2"><span style="font-size:12.0pt;color:black;background:white">In the first part of this lecture, we introduce some basic definitions and concepts of functional analysis like, e.g., Fredholm
operators, spectra and functional calculus. </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span class="contentpasted2"><span style="font-size:12.0pt;color:black;background:white">The second part deals with different topologies on the space of self-adjoint Fredholm operators, for which the spectral flow
induces an isomorphism between their fundamental groups and the integers.</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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