var sms = '<div id="sms_bulletin">  <div id="sms_header">  <div class="do_not_print" id="arrow_left"><a href="?next=-58"><img src="//www2.math.ethz.ch/smsjs/images/arrow_left.png"/></a></div><div class="do_not_print" id="arrow_right"><a href="?next=-56"><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. 3</span>      <span style="float: right; text-align:right; width: 250px;">19.6 - 23.6.2023</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, June 19      </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, June 20      </div>      <div class="day_content">        <div class="day_content_item normal"><div class="event_location uni_ge"><a class="external" href="https://unige.ch">Université de Genève</a></div><div class="event_type"><a class="external" href="https://www.unige.ch/math/annonces/seminaire-danalyse-numerique">Séminaire d\'Analyse Numérique </a></div><br /><div class="event_speaker"> Paolo Ricci (EPF Lausanne)</div><div class="event_title">Title T.B.A.</div><div class="event_time">14:00 &bull; Université de Genève, Conseil Général 7-9, Room 1-05</div>        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Wednesday, June 21      </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/talks-in-financial-and-insurance-mathematics">Talks in Financial and Insurance Mathematics</a></div><br /><div class="event_speaker"><a class="external" href="http://www.ajentzen.de/">Prof. Dr. Arnulf Jentzen (The Chinese University of Hong Kong, Shenzhen and University of Münster)</a></div><div class="event_title">Overcoming the curse of dimensionality: from nonlinear Monte Carlo to the training of neural networks <span class="abstract-button do_not_print">abstract</span></div><div class="abstract-text" style="display: none"><strong>Abstract:</strong><br />Partial differential equations (PDEs) are among the most universal tools used in modelling problems in nature and man-made complex systems. Nearly all traditional approximation algorithms for PDEs in the literature suffer from the so-called "curse of dimensionality" in the sense that the number of required computational operations of the approximation algorithm to achieve a given approximation accuracy grows exponentially in the dimension of the considered PDE. With such algorithms it is impossible to approximatively compute solutions of high-dimensional PDEs even when the fastest currently available computers are used. In the case of linear parabolic PDEs and approximations at a fixed space-time point, the curse of dimensionality can be overcome by means of Monte Carlo approximation algorithms and the Feynman-Kac formula. In this talk we present an efficient machine learning algorithm to approximate solutions of high-dimensional PDE and we also prove that deep artificial neural network (ANNs) do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs. Moreover, we specify concrete examples of smooth functions which can not be approximated by shallow ANNs without the curse of dimensionality but which can be approximated by deep ANNs without the curse of dimensionality. In the final part of the talk we present some recent mathematical results on the training of neural networks.</div><div class="event_time">17:15 &bull; ETH Zentrum, R&auml;mistrasse 101, Z&uuml;rich, Building HG, Room G 43</div>        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Thursday, June 22      </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/talks-in-mathematical-physics">Talks in Mathematical Physics</a></div><br /><div class="event_speaker"> Sergei Merkulov (Uni Luxembourg)</div><div class="event_title">On the interrelations between graph complexes <span class="abstract-button do_not_print">abstract</span></div><div class="abstract-text" style="display: none"><strong>Abstract:</strong><br />We study Maxim Kontsevich\'s graph complex as well as its oriented and targeted versions, and show a new proof of the theorems due to Thomas Willwacher and Marko Zivkovic stating isomorphisms of their cohomology groups. Both theorems follow from one and the same surprisingly short argument.</div><div class="event_time">15:15 &bull; ETH Zentrum, R&auml;mistrasse 101, Z&uuml;rich, Building HG, Room G 43</div>        </div>        <div class="day_content_item normal"><div class="event_location uni_ba"><a class="external" href="https://unibas.ch">Universität Basel</a></div><div class="event_type"><a class="external" href="https://www.ntwebseminar.org/">Number Theory Web Seminar</a></div><br /><div class="event_speaker"> Efthymios Sofos (University of Glasgow)</div><div class="event_title">The second moment method for rational points <span class="abstract-button do_not_print">abstract</span></div><div class="abstract-text" style="display: none"><strong>Abstract:</strong><br />In a joint work with Alexei Skorobogatov we used a second-moment approach to prove asymptotics for the average of the von Mangoldt function over the values of a typical integer polynomial. As a consequence, we proved Schinzel\'s Hypothesis in 100% of the cases. In addition, we proved that a positive proportion of Châtelet equations have a rational point. I will explain subsequent joint work with Tim Browning and Joni Teräväinen [arXiv:2212.10373] that develops the method and establishes asymptotics for averages of an arithmetic function over the values of typical polynomials. Part of the new ideas come from the theory of averages of arithmetic functions in short intervals. One of the applications is that the Hasse principle holds for 100% of Châtelet equations. This agrees with the conjecture of Colliot-Thélène stating that the Brauer--Manin obstruction is the only obstruction to the Hasse principle for rationally connected varieties.</div><div class="event_time">17:00 &bull; Universität Basel, online Seminar</div>        </div>      </div>    </div>    <div class="day">      <div class="day_title">        Friday, June 23      </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>';