<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=""><meta http-equiv="Content-Type" content="text/html; charset=utf-8" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">皆様</div><div class=""><br class=""></div><div class="">来週に以下の連続講演 (online) が予定されております。</div><div class="">世話人である Satoshi Nawata氏 (Fudan University) からの依頼により代理で投稿させて頂きます。</div><div class="">Zoom ID や パスワードは以下のサイトにも情報が掲載されていますのでご確認下さい。</div><div class=""><br class=""></div><div class=""><a href="https://researchseminars.org/seminar/Milanov" class="">https://researchseminars.org/seminar/Milanov</a></div><div class=""><br class=""></div><div class="">どうぞよろしくお願いします。</div><div class=""><br class=""></div><div class="">東京大学大学院数理科学研究科</div><div class="">岩木耕平</div><br class=""><div class=""><br class=""><blockquote type="cite" class=""><div class="">転送されたメッセージ:</div><br class="Apple-interchange-newline"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">差出人: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Satoshi Nawata <<a href="mailto:snawata@gmail.com" class="">snawata@gmail.com</a>><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">件名: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class=""><b class="">can you share this info in math community?</b><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">日付: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">2020年11月14日 23:25:56 JST<br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">宛先: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Kohei_Iwaki <<a href="mailto:iwaki@ms.u-tokyo.ac.jp" class="">iwaki@ms.u-tokyo.ac.jp</a>><br class=""></span></div><br class=""><div class=""><div dir="ltr" class=""><div class="gmail-" style="font-family:system-ui,-apple-system,system-ui,".SFNSText-Regular",sans-serif;color:rgb(28,30,33);font-size:12px;white-space:pre-wrap"><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Dear Kohei, </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">I wonder if you could share a lecture series by Milanov in Japanese math community. Thanks in advance. </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Speaker: Todor Milanov (IPMU)</div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Title: Towards Hirota Bilinear Equations in Gromov--Witten theory</div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Time: 15:30--17:00, Nov 16-20 (Mon-Fri)</div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Zoom ID: 9383671691 Password: 123456</div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">If the quantum cohomology of a smooth projective variety X, or more generally a projective variety with an orbifold structure, is semisimple, then Dubrovin and Zhang have constructed an integrable hierarchy that governs the Gromov--Witten (GW) invariants of X. The main motivation for the work that I would like to present is to construct an infinite dimensional Grassmannian that parametrizes the solutions of the Dubrovin--Zhang hierarchies. Similar description was proposed first by Mikio Sato for the KP hierarchy and it is very useful, because it allows us to study integrable hierarchies via the methods of representation theory of infinite dimensional Lie algebras. Based on ideas of Givental, I developed a method for proving that the generating function of GW invariants satisfies a given system of Hirota Bilinear Equations (HBEs). This is exactly what I am planning to talk about in my lectures. Note however, that the existence of the HBEs is still not clear. Based on joint work with B. Bakalov, I can only speculate that the HBEs, if they exist at all, should come from the representation theory of a certain class of lattice vertex algebras, i.e., in principal, we have reduced the problem of constructing HBEs in GW theory to a problem about lattice vertex algebras. Our ideas with Bakalov should be tested in an interesting example, such as, X=CP^2 or X= orbifold structure on P^1 with negative orbifold Euler characteristics. At this point I am not ready to lecture about the relation to lattice VOA, but if time permits, I will try to say something. Here is a list of topics that I am planning to cover </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">1. Frobenius manifolds and quantum cohomology </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">2. Givental's higher genus reconstruction </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">3. Quantization formalism </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">4. Vertex operators and phase factors </div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">5. Hirota Bilinear Equations: an example.<br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit"><br class=""></div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Best,</div><div class="gmail-_1mj gmail-_1mf" style="font-family:inherit">Satoshi</div></div></div>
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