<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">幾何学分科会メーリングリストの皆様</div><div class=""><br class=""></div><div class="">数理解析研究所に滞在中の Katrin Leschke 氏と Franz Pedit 氏による minicourses を</div><div class="">以下のように計画しました。 </div><div class=""><div class=""><br class=""></div><div class="">Prof. Katrin Leschke <font face="Osaka" class=""> </font><span class="" style="font-family: Osaka;">Integrable system methods in smooth and discrete surface theory</span></div><div class=""><span class="" style="font-family: Osaka;">Prof. Franz Pedit </span><span class="" style="font-family: Osaka;">Higgs bundles, harmonic maps, and differential geometry of surfaces</span></div><div class=""><span class="" style="font-family: Osaka;"><br class=""></span></div><div class=""><div class="">5月6日 13:30-15:00 Leschke 15:30-17:00 Pedit </div><div class="">5月7日 10:00-11:30 Leschke 13:30-15:00 Pedit 15:30-17:00 Leschke </div><div class="">5月8日 10:00-11:30 Pedit </div></div><div class=""><br class=""></div></div><div class="">興味のある方は、以下のページから登録 (5月3日締め切り) をお願いします。</div><div class=""><br class=""></div><div class=""><a href="https://docs.google.com/forms/d/e/1FAIpQLSem8yi_2UEoZBgWuYCkRstkg-5K56jbzDNDyZF-IPiTXKjBqw/viewform?usp=sf_link" class="">https://docs.google.com/forms/d/e/1FAIpQLSem8yi_2UEoZBgWuYCkRstkg-5K56jbzDNDyZF-IPiTXKjBqw/viewform?usp=sf_link</a></div><div class=""><br class=""></div><div class="">前日までに登録された email address に zoom meeting の情報を送ります。</div><div class=""><br class=""></div><div class="">大仁田義裕 (OCAMI) </div><div class="">小野 薫 (RIMS)</div><div class=""><br class=""></div><div class=""><div class=""><br class=""></div></div><div class="gmail_default"><font face="Osaka" class=""><span class="">=="</span>Integrable system methods in smooth and discrete surface theory” by Prof. Leschke</font><span class="" style="font-family: Osaka;">==</span></div><div class="gmail_default"><span class="" style="font-family: Osaka;">Abstract: </span></div><div class="gmail_default"><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">In this lecture series we will explore how integrable system methods can </font></span><span class="" style="font-family: Osaka;">be applied </span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class="" style="font-family: Osaka;">in smooth and discrete surface theory. A core ingredient for this discussion </span><span class="" style="font-family: Osaka;">is </span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class="" style="font-family: Osaka;">the associated family of at connections. For example, for surfaces with constant</span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">non-vanishing mean curvature (CMC), the Gauss map is harmonic by the Ruh-Vilms</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">theorem: this is equivalent to the flatness of a complex family of connections. We will</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">discuss how an integrable structure gives rise to a variety of transformations given by</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">parallel sections of the associated family, e.g., the so-called associated family of surfaces,</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">the simple factor dressing and the Darboux transformation. In particular, we will discuss</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">the interplay between three distinct integrable systems associated to a CMC surface and</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">global properties of the transforms.</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">As an application, we will discuss the Darboux transforms of Delaunay surfaces, that</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">is, CMC surfaces of revolution. We obtain new CMC cylinder as well as same-lobed</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">CMC multibubbletons.</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">If time permits, we will discuss how the smooth approaches can be discretised in</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">the example of a discrete polarised curve. We will introduce a discrete equivalent to</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">the associated family of at connections and discuss closing conditions of its Darboux</font></span></div><div class="" style="margin: 0px; font-stretch: normal; line-height: normal;"><span class=""><font face="Osaka" class="">transforms. </font></span></div></div><div class="gmail_default"><font face="Osaka" class=""><br class=""></font></div><div class="gmail_default"><div class=""><span class=""><font face="Osaka" class="">=="</font></span><font face="Osaka" class="">Higgs bundles, harmonic maps, and differential geometry of surfaces” </font><span class="" style="font-family: Osaka;">by Prof. Franz Pedit==</span></div><div class=""><div class="gmail_default"><span class="" style="font-family: Osaka;">Abstract: </span></div><div class="gmail_default"><font face="Osaka" class="">Higgs bundles arise in a number of ways: as a 2-dimensional reduction of </font></div><div class="gmail_default"><font face="Osaka" class="">the 4-dimensional self-dual Yang-Mills equations; as the equations for harmonic </font><span class="" style="font-family: Osaka;">maps </span></div><div class="gmail_default"><span class="" style="font-family: Osaka;">into a symmetric space; as a zero curvature equation for a suitable connection; </span></div><div class="gmail_default"><font face="Osaka" class="">as a representation of the fundamental group of a compact surface. These different </font></div><div class="gmail_default"><font face="Osaka" class="">incarnations relate aspects of mathematical physics, PDEs, differential/complex/symplectic </font></div><div class="gmail_default"><span class="" style="font-family: Osaka;">geometry and topology. I will attempt to explain some of these connections and how they </span></div><div class="gmail_default"><span class="" style="font-family: Osaka;">can be used to understand problems arising in differential geometry. In addition to providing </span></div><div class="gmail_default"><span class="" style="font-family: Osaka;">a more overarching picture, I will also discuss some examples. </span></div><div class="gmail_default"><br class=""></div></div></div><div class="">
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