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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Next week we have the next edition of the DDT&G. Please see the announcement below. Please let interested master students know.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Of course we will also have an AG on Tuesday. Lies will talk about Extremal Betti Numbers. Abstract below.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;mso-fareast-language:EN-US">Thomas<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Dear colleagues, <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">You are cordially invited to attend the next Dutch Differential Topology and Geometry seminar, which will take place next week in Leiden. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Speaker</span></b><span style="color:black">:
<a href="https://guyboyde.wordpress.com/" title="https://guyboyde.wordpress.com">
Guy Boyde</a><o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Title</span></b><span style="color:black">: "<i>The homology of Temperley-Lieb algebras"
</i>(see below for the abstract)<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Date</span></b><span style="color:black">: Friday 7 March, 14:30-17:00<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Location</span></b><span style="color:black">: Leiden, BW.0.32 (Gorleaus)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">The schedule will be as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">Please notice that the first part of the seminar (2:30-3:30 p.m.) is intended for general mathematical audience, and master students with an interest in geometry and topology are especially encouraged to participate.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><br>
</span><u><span style="color:blue"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link.">https://www.few.vu.nl/~trt800/</a></span></u><u><span style="color:#070706"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link."><span style="color:#070706">ddt</span></a></span></u><u><span style="color:blue"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link.">g.html</a></span></u><o:p></o:p></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">We hope to see many of you next week!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Alvaro, Federica and Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Abstract</span></b><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> Temperley-Lieb algebras are certain (very pictorial) finite-dimensional associative algebras coming originally from statistical physics and knot theory. There are several ways to define homology groups for an
algebra: we will focus on just one. The punchline of the talk is that the homology of Temperley-Lieb algebras has a rich algebraic structure coming from the "geometry" of the original algebras.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> In the first half of the talk, I'll give a friendly introduction to these algebras: we'll see why they're important in knot theory, and prove that their dimension is given by the Catalan numbers. We'll also discuss
the homological algebra that we will need in the rest of the talk (which will be very elementary and hands on). In the second talk I'll explain what we know about their homology, ending with joint work in progress with Rachael Boyd, Oscar Randal-Williams,
and Robin Sroka.<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">AG: 4-3-2025 11:00 Lies Beers: Extremal Betti Numbers<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
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<span style="font-size:9.0pt;font-family:Helvetica;color:black">[Joint work with Magnus Botnan] Let T(n,k+1) be the Turan graph with n vertices and k+1 partition classes. We study extremal Betti numbers and persistence in edgewise filtrations of flag complexes.
For a graph G on n vertices, the kth Betti number of its flag complex is maximized when G = T(n,k+1). Extending this, we construct an edgewise filtration in which each graph attains the maximal kth Betti number among all graphs with the same number of edges.
Moreover, the persistence barcode achieves the maximal number of intervals and total persistence among all edgewise filtrations with |E(T(n,k+1))| edges.<o:p></o:p></span></p>
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<span style="font-size:9.0pt;font-family:Helvetica;color:black">For k=1, we analyze edgewise filtrations of the complete graph. The maximal number of barcode intervals occurs precisely when T(n,2) appears in the filtration. Among these, we characterize those
achieving maximal total persistence. We also prove that no filtration optimizes the first Betti number for all graphs in the filtration and conjecture that our constructions maximize total persistence over all edgewise filtrations of the complete graph.<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
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