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<p class="MsoNormal"><span style="color:black">Dear all, <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 Utrecht. This will be the last meeting before the summer break. <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://www.math.purdue.edu/~snariman/" title="https://www.math.purdue.edu/~snariman/">Sam Nariman</a> (Purdue University)<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Title</span></b><span style="color:black">: Part 1:
<i>Mather-Thurston Theory and Diffeomorphism Groups </i> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> Part 2: <i>Flat Bundles, PL Foliations, and Bounded Cohomology </i><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> (see below for the abstracts)<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Date</span></b><span style="color:black">: Friday 27 June, 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">: Utrecht, KBG Atlas (Koningsbergergebouw)<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><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><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">Abstracts</span></b><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="elementtoproof" style="margin-left:36.0pt;text-indent:0cm;mso-list:l1 level1 lfo2">
<![if !supportLists]><span style="font-size:11.0pt;color:#242424"><span style="mso-list:Ignore">1.<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><i><span style="font-size:11.0pt;color:#242424">Mather–Thurston Theory and Diffeomorphism Groups</span></i><span style="font-size:11.0pt;color:#242424"><o:p></o:p></span></p>
<p class="elementtoproof"><o:p> </o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">I will discuss a remarkable theorem of Thurston, extending earlier work of Mather, which relates the identity component of diffeomorphism groups to the classifying space of Haefliger groupoids—objects
that encode the local behavior of foliations. This classifying space plays a central role in the homotopy theory of foliations, yet its homotopy type remains elusive and difficult to compute.</span><o:p></o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">Mather–Thurston theory provides a bridge between the homology of diffeomorphism groups and the homotopy groups of Haefliger spaces. While this result is an h-principle-type theorem, it stands
out for reversing the usual philosophy: it uses the more “rigid” structure of diffeomorphism groups to probe the more “flexible,” homotopy-theoretic structure of Haefliger spaces.</span><o:p></o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">I will explain Thurston’s method and how it can be adapted to prove analogous results for other subgroups of diffeomorphism groups—cases that had previously only been conjectured. Unlike
many h-principle arguments, which first analyze the local case M = \mathbb{R}^n before globalizing, Thurston’s original proof is intrinsically compactly supported. This makes it particularly effective when local results are hard to obtain, for example, for
volume-preserving diffeomorphisms or contactomorphisms.</span><o:p></o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">If time permits, I will also discuss PL foliations and, as an application, show how Mather–Thurston theory can be applied in the usual (flexibility-first) h-principle direction to prove
the perfectness of the identity component of the PL homeomorphism group of compact surfaces.</span><o:p></o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424"> </span><o:p></o:p></p>
<p class="elementtoproof" style="margin-left:36.0pt;text-indent:0cm;mso-list:l0 level1 lfo4">
<![if !supportLists]><span style="font-size:11.0pt;color:#242424"><span style="mso-list:Ignore">2.<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><i><span style="font-size:11.0pt;color:#242424">Flat Bundles, PL Foliations, and Bounded Cohomology</span></i><span style="font-size:11.0pt;color:#242424"><o:p></o:p></span></p>
<p class="elementtoproof"><o:p> </o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">Depending on how far we get in the first talk, I will explore connections between Mather–Thurston theory, PL homeomorphisms, and bounded cohomology, focusing on applications to flat bundles
and geometric inequalities. A central theme will be the Milnor–Wood inequality, which bounds the Euler number of flat S^1-bundles over surfaces. Originally established by Milnor for linear representations and later extended by Wood to nonlinear flat circle
bundles, this inequality reveals deep relationships between dynamics, topology, and bounded cohomology.</span><o:p></o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">I will begin with a brief overview of the classical inequality and its reinterpretation through the lens of bounded cohomology, as developed by Gromov. Then, I will connect it to a controlled
version of Mather–Thurston theory, due to Freedman.</span><o:p></o:p></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424">These ideas also inform recent results that clarify the limits of the Milnor–Wood inequality in higher dimensions, particularly for non-linear flat bundles modeled on the diffeomorphism
group of manifolds of dimensions higher than one. I will present new constructions showing the failure of boundedness for the Euler class in some of these cases.</span><o:p></o:p></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="elementtoproof"><span style="font-size:11.0pt;color:#242424"> </span><o:p></o:p></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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