<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:Helvetica;
panose-1:0 0 0 0 0 0 0 0 0 0;}
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Aptos;
panose-1:2 11 0 4 2 2 2 2 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
font-size:12.0pt;
font-family:"Aptos",sans-serif;
mso-ligatures:standardcontextual;}
span.EmailStyle19
{mso-style-type:personal-reply;
font-family:"Aptos",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;
mso-ligatures:none;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 72.0pt 72.0pt 72.0pt;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="en-NL" link="#467886" vlink="#96607D" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">There is a trainstrike tomorrow, however we decided to still continue with Samuels talk.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">It will, by exception, be streamed. A zoomlink will be send tomorrow.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">From:
</span></b><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">"Rot, T.O. (Thomas)" <t.o.rot@vu.nl><br>
<b>Date: </b>Friday, 6 June 2025 at 15:38<br>
<b>To: </b>"_list_topology.beta" <topology.beta@listserver.vu.nl><br>
<b>Subject: </b>CTAAAG tuesday<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="mso-ligatures:none"><o:p> </o:p></span></p>
</div>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Samuel is going to talk about his research. See abstract and title below. The format has slightly changed. Talks will be about an hour, with time for questions after.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Are there any other PhD students that want to discuss their research the coming weeks?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:3.75pt;margin-right:0cm;margin-bottom:7.5pt;margin-left:0cm;background:white">
<b><span style="font-size:11.5pt;font-family:Helvetica;color:black;mso-ligatures:none">AG:10-06-2025: Samuel: Spectral systems and connection matrices<o:p></o:p></span></b></p>
<p class="MsoNormal" style="margin-bottom:3.75pt;line-height:13.5pt;background:white">
<span style="font-size:9.0pt;font-family:Helvetica;color:black;mso-ligatures:none">Spectral sequences and systems are tools from algebraic topology widely known and used in the study of homology and fibrations. These usually arise form an exact couple system,
having a filtration on a space associated.<br>
Parallel to this, connection matrices were developed in the realm of applied topology for qualitative study of dynamical systems. We have a Morse decomposition of a system, and the relative homologies being the Conley index provide us information about it.
These two wildly different ideas turn out to be two faces of the same coin. We see how these connection matrices are at its core just a spectral system, and how given an exact couple system one can build a connection matrix and thus a space that generates
it with the relative homologies.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
</body>
</html>