var sms = '<div id="sms_bulletin">  <div id="sms_header">  <div class="do_not_print" id="arrow_left"><a href="?next=-130"><img src="//www2.math.ethz.ch/smsjs/images/arrow_left.png"/></a></div><div class="do_not_print" id="arrow_right"><a href="?next=-128"><img src="//www2.math.ethz.ch/smsjs/images/arrow_right.png"/></a></div>    <div class="sms_title">      <span style="float: left;">SMS</span>      <span>SWISS MATHEMATICAL SOCIETY</span>      <span style="float: right;">SMG</span>    </div>    <div class="sms_info">      <span style="float: left; width: 250px;">Bulletin no. 8</span>      <span style="float: right; text-align:right; width: 250px;">24.7 - 28.7.2023</span>      <span style="text-align: center; display: block; width: 250px; margin: auto; position: relative;">Summer Break 2023</span>    </div>  </div>  <div></div>  <div id="sms_content">    <div class="day">      <div class="day_title">        Monday, July 24      </div>      <div class="day_content">        <div class="day_content_item no_event">        No events scheduled today!        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Tuesday, July 25      </div>      <div class="day_content">        <div class="day_content_item no_event">        No events scheduled today!        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Wednesday, July 26      </div>      <div class="day_content">        <div class="day_content_item normal"><div class="event_location uni_zh"><a class="external" href="https://ethz.ch">ETH Z&uuml;rich</a></div><div class="event_type"><a class="external" href="https://math.ethz.ch/s/daco-seminar">DACO Seminar</a></div><br /><div class="event_speaker">Prof. Dr. Neil Olver (London School of Economics and Political Science, London, UK)</div><div class="event_title">Thin trees for laminar families <span class="abstract-button do_not_print">abstract</span></div><div class="abstract-text" style="display: none"><strong>Abstract:</strong><br />In the strong form of the thin tree conjecture, formulated by Goddyn in 2004, we are given a k-edge-connected graph and wish to find a tree containing at most an O(1/k) fraction of the edges across every cut. This conjecture, if true, has a variety of implications in a number of areas such as graph theory and approximation algorithms. A natural relaxation of this problem is to find a tree with at most O(1/k) edges across a fixed collection of cuts, instead of all cuts. Using iterative relaxation, combined with a simple reduction technique, we show that the thin tree conjecture is true whenever the specified cuts form a laminar family.Joint work with Nathan Klein.</div><div class="event_time">10:00 &bull; ETH Zentrum, R&auml;mistrasse 101, Z&uuml;rich, Building HG, Room G 19.2</div>        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Thursday, July 27      </div>      <div class="day_content">        <div class="day_content_item normal"><div class="event_location uni_zh"><a class="external" href="https://ethz.ch">ETH Z&uuml;rich</a></div><div class="event_type"><a class="external" href="https://math.ethz.ch/s/daco-seminar">DACO Seminar</a></div><br /><div class="event_speaker">Dr. Martin Nägele (University of Bonn)</div><div class="event_title">An Improved Approximation Guarantee for Prize-Collecting TSP <span class="abstract-button do_not_print">abstract</span></div><div class="abstract-text" style="display: none"><strong>Abstract:</strong><br />We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may choose to not include a vertex of the input graph in the returned tour at the cost of a given vertex-dependent penalty, and the objective is to balance the length of the tour and the incurred penalties for omitted vertices by minimizing the sum of the two. We present an algorithm that achieves an approximation guarantee of 1.774 with respect to the natural linear programming relaxation of the problem. This significantly reduces the gap between the approximability of classical TSP and PCTSP, beating the previously best known approximation factor of 1.915. As a key ingredient of our improvement, we present a refined decomposition technique for solutions of the LP relaxation, and show how to leverage components of that decomposition as building blocks for our tours.This is joint work with Jannis Blauth.</div><div class="event_time">10:00 &bull; ETH Zentrum, R&auml;mistrasse 101, Z&uuml;rich, Building HG, Room G 19.1</div>        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Friday, July 28      </div>      <div class="day_content">        <div class="day_content_item no_event">        No events scheduled today!        </div>      </div>    </div>  </div>  <div id="sms_footer">    address: Alessandra Naldi Windler, Departement Mathematik, HG G 51.4, ETH Zurich, Raemistrasse 101, CH-8092 Zurich<br />    email: <a href="mailto:bulletin@math.ch">bulletin@math.ch</a> | phone: +41 44 632 3684 | url: <a href="https://math.ch">https://math.ch</a>    <br /><br /><img src="//www2.math.ethz.ch/smsjs/sms_logo.gif" width="150" alt="SMS/SMG Logo" title="SMS/SMG Logo" />  </div></div>';