<div dir="ltr"><div class="gmail_quote"><div style="word-wrap:break-word;line-break:after-white-space"><div>Carissimi,</div><div> su suggerimento del Prof. Francesco Caravenna, che ringrazio, </div><div>vi inoltro la presentazione di un corso di dottorato in modalita' online </div><div>che puo' risultare interessante per alcuni di voi.</div><div>Cordiali saluti,</div><div>PC</div><div><br><blockquote type="cite"><div>Inizio messaggio inoltrato:</div><br><div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px"><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif;color:rgba(0,0,0,1.0)"><b>Da: </b></span><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif">Stefania Ugolini <<a href="mailto:stefania.ugolini@unimi.it" target="_blank">stefania.ugolini@unimi.it</a>><br></span></div><div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px"><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif;color:rgba(0,0,0,1.0)"><b>Oggetto: </b></span><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif"><b>[Random] Graduate course in February</b><br></span></div><div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px"><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif;color:rgba(0,0,0,1.0)"><b>Data: </b></span><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif">30 gennaio 2021 16:52:49 CET<br></span></div><div style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px"><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif;color:rgba(0,0,0,1.0)"><b>A: </b></span><span style="font-family:-webkit-system-font,Helvetica Neue,Helvetica,sans-serif">random <<a href="mailto:random@fields.dm.unipi.it" target="_blank">random@fields.dm.unipi.it</a>><br></span></div><br><div><div style="font-family:"Times New Roman";font-size:inherit"><div><div style="font-size:2ex;line-height:2.8ex"><p class="MsoNormal" style="line-height:normal"><font face="Arial, sans-serif" size="3">Università degli Studi di Milano: PhD program</font></p><p class="MsoNormal" style="font-size:2ex;line-height:normal"><b><span lang="EN-GB" style="font-size:14pt;font-family:Arial,sans-serif"><br></span></b></p><p class="MsoNormal" style="font-size:2ex;line-height:normal"><b><span lang="EN-GB" style="font-size:14pt;font-family:Arial,sans-serif">Stochastic quantization of the Euclidean quantum field theory<u></u><u></u></span></b></p><p class="MsoNormal" style="font-size:2ex;line-height:normal"><b><span lang="EN-GB" style="font-size:14pt;font-family:Arial,sans-serif"><br></span></b></p><p class="MsoNormal" style="font-size:2ex;line-height:normal"><span lang="EN-GB" style="font-size:14pt;font-family:Arial,sans-serif">Lecturer<b>: Prof. Dr. Massimiliano Gubinelli</b></span></p></div><div style="font-size:2ex;line-height:2.8ex"><br></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">The goal of Euclidean quantum field theory is to build probability<br>measures on the space of distributions satisfying properties such as<br>Euclidean invariance, reflection positivity and non-triviality, that<br>allows to recover an interacting relativistic quantum field satisfying<br>Wightman axioms. </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">Stochastic quantization, first proposed by Parisi–Wu and Nelson, </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">is a method of construction of such measures via stationary solutions </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">of a stochastic partial differential equations driven by additive </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">Gaussian white noise.</font><br><br><font size="4">In this course we will learn about the stochastic quantization of the<br>Euclidean quantum field theory of a scalar boson with quartic<br>interaction and its main properties. We introduce the Φ43 measure </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">as the limit of the invariant measure of a finite dimensional system </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">of stochastic differential equations. </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">The proof proposed uses several analytic and probabilistic techniques,<br>such as white noise analysis, weighted Besov spaces on lattice and<br>paraproducts, which also find applications in other problems arising<br>in the study of deterministic and stochastic singular differential<br>equations. </font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4"><br></font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">All these tools and ideas will be gradually introduced and<br>explained during the lectures. The course is as much as possible<br>self-contained and requires as a prerequisite only basic knowledge of<br>stochastic and functional analysis. </font><br><br></div><div style="font-size:2ex;line-height:2.8ex"><span style="font-size:2ex"><br></span></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">Scheduling: <b>February</b> <b>15, 16, 18, 22, 25</b> from 10:00 to 12:00 and from 14:00 to 16:00</font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4"><br></font></div><div style="font-size:2ex;line-height:2.8ex"><font size="4">Online via Zoom (see the following link)</font></div><div><br></div><div><span style="font-size:11pt;line-height:15.6933px;font-family:Arial,sans-serif">Course page: </span><span style="font-size:11pt;line-height:15.6933px;font-family:Calibri,sans-serif"><span style="font-size:10.5pt;line-height:14.98px"><a href="https://www.iam.uni-bonn.de/abteilung-gubinelli/sq-lectures-milan-ws2021" target="_blank">https://www.iam.uni-bonn.de/abteilung-gubinelli/sq-lectures-milan-ws2021</a></span></span></div><div><span style="font-size:11pt;line-height:15.6933px;font-family:Calibri,sans-serif"><br></span></div></div></div>
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