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<p class="MsoNormal"><span lang="EN-US">Dear colleagues,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><br>
Please see the announcement below. The spectral flow is a nice topological tool for differential equations.
<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">I therefore hope to see not only topologists, but also dynamicists in the audience.
<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">Please note that the talks should be accessible to master students. Please forward this to any master students that might be interested. <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"><span lang="EN-US"><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>Wednesday, 5 April 2023 at 18:17<br>
<b>To: </b>Federica Pasquotto <f.pasquotto@math.leidenuniv.nl><br>
<b>Subject: </b>DDT&G seminar on April 14 in Amsterdam: Nils 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="contentpasted0"><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="contentpasted0"><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="contentpasted0"><span style="font-size:12.0pt;color:black">You are kindly invited to attend the next Dutch Differential Topology and Geometry seminar:</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><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="contentpasted0"><b><span style="font-size:12.0pt;color:black">Speaker</span></b></span><span class="contentpasted0"><span style="font-size:12.0pt;color:black">: Niels Waterstraat (MLU Halle-Wittenberg)</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:black">Title</span></b></span><span class="contentpasted0"><span style="font-size:12.0pt;color:black">: <i>"Spaces of Self-adjoint Fredholm Operators and the Spectral
Flow" </i>(see below for the abstract)</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:black">Date</span></b></span><span class="contentpasted0"><span style="font-size:12.0pt;color:black">: Friday 14 April, 14:00-16:30</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><b><span style="font-size:12.0pt;color:black">Location</span></b></span><span class="contentpasted0"><span style="font-size:12.0pt;color:black">: VU Amsterdam, NU building, room 9-A46</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><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="contentpasted3"><span style="font-size:12.0pt;color:black;background:white">It will also be possible to attend remotely </span></span><span class="contentpasted3"><span style="font-size:12.0pt;color:black">(login details
to be provided shortly). </span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">The schedule will be as follows:</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><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="contentpasted0"><span style="font-size:12.0pt;color:black">2:00-3:00 p.m.: first part of the seminar (little to no prior knowledge assumed)</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">3:30-4:30 p.m.: second part of the seminar (slightly more advanced level)</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><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="contentpasted0"><span style="font-size:12.0pt;color:black;background:white">Master students with an interest in topology and geometry are strongly encouraged to participate!</span></span><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>
<p style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:</span></span><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"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank">https://www.few.vu.nl/~trt800/<span style="color:#070706;background:#FFEE94">ddt</span>g.html</a><o:p></o:p></span></p>
<p style="background:white"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
<p style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">We would also like to remind you that most of the previous lectures are available on the YouTube channel of the seminar: </span></span><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"><a href="https://www.youtube.com/channel/UCN0o3PUqaC_ZhPNuM846kgg/" target="_blank" title="Original URL: https://www.youtube.com/channel/UCN0o3PUqaC_ZhPNuM846kgg/. Click or tap if you trust this link.">https://www.youtube.com/channel/UCN0o3PUqaC_ZhPNuM846kgg/</a><o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">
<o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><span style="font-size:12.0pt;color:black">We hope to see many of you next week!</span></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
<p style="background:white"><span class="contentpasted0"><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="contentpasted0"><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="contentpasted0"><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 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.<o:p></o:p></span></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">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.
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.<o:p></o:p></span></p>
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