<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>皆様<br class=""><br class="">複素解析幾何セミナー@東大数理のご案内です。<br class=""><h3 style="margin: 3px 0px 8px; padding: 5px 0px; font-family: メイリオ, Meiryo, "ヒラギノ角ゴ Pro W3", "Hiragino Kaku Gothic Pro", Osaka, "ＭＳ Ｐゴシック", "MS PGothic", Helvetica, Arial, sans-serif; font-size: 14px; font-stretch: inherit; line-height: inherit; vertical-align: baseline; border-top-width: 1px; border-top-style: dotted; border-top-color: rgb(33, 127, 196); border-bottom-width: 1px; border-bottom-style: dotted; border-bottom-color: rgb(33, 127, 196); overflow: hidden; caret-color: rgb(51, 51, 51); color: rgb(51, 51, 51);" class="">2020年07月13日(月)</h3><div class="seminar_naiyo" style="margin: 0px 0px 20px; padding: 0px; font-family: メイリオ, Meiryo, "ヒラギノ角ゴ Pro W3", "Hiragino Kaku Gothic Pro", Osaka, "ＭＳ Ｐゴシック", "MS PGothic", Helvetica, Arial, sans-serif; font-size: 13px; font-stretch: inherit; line-height: inherit; vertical-align: baseline; caret-color: rgb(51, 51, 51); color: rgb(51, 51, 51);">10:30-12:00 Zoom開催<br class=""><strong style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline;" class="">井上瑛二 氏</strong> (東大数理)<br class=""><span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-1-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-2" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-3" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>-cscK metrics and <span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-2-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-4" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-5" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-6" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>K-stability of polarized manifolds<br class=""><div class="waku" style="margin: 5px 0px 8px; padding: 9px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; border: 1px solid rgb(204, 204, 204); background-color: rgb(239, 239, 239);">[ 講演概要 ]<br class="">I firstly talk about some backgrounds on the following two frameworks; "cscK metrics & K-stability" and "Kähler-Ricci soliton & modified K-stability", whose intersection is precisely the framework on "Kähler-Einstein metrics & K-stability". <br class="">I will introduce a new framework unifying these frameworks, which I call the framework on "<span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-3-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-7" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-8" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-9" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>-cscK metrics and <span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-4-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-10" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-11" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-12" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>K-stability". <br class=""><br class="">There are two divided contents: <br class="">1. I explain formulation and first motivation for <span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-5-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-13" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-14" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-15" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>-cscK metrics and give brief remarks on results parallel to those for cscK metrics / Kähler-Ricci solitons. I will illustrate some attractive features/phenomenon special to <span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-6-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-16" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-17" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-18" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>-cscK metrics by examples; "extremal limit" and "phase transition". <br class="">(cf. <a href="https://arxiv.org/abs/1902.00664" class="">https://arxiv.org/abs/1902.00664</a>)<br class="">2. I explain how one should/can formulate/derive/express <span class="MathJax_Preview" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; color: inherit;"></span><span id="MathJax-Element-7-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math>" role="presentation" style="margin: 0px; padding: 1px 0px; font-family: inherit; font-size: 15.989999771118164px; font-variant-caps: inherit; font-stretch: inherit; line-height: 0; vertical-align: baseline; display: inline-block; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;"><span id="MJXc-Node-19" class="mjx-math" aria-hidden="true" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-20" class="mjx-mrow" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-21" class="mjx-mi" style="margin: 0px; padding: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="margin: 0px; padding: 0.191em 0px 0.503em; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; display: block; white-space: pre; box-sizing: content-box !important;">μ</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="margin: 0px; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: inherit; vertical-align: baseline; top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; padding: 1px 0px 0px !important; position: absolute !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span>-Futaki invariant of test configurations with general singularities. We also construct a characteristic class for families of polarized schemes, which generalizes the CM line bundle in K-stability. I also give a few words on applications to moduli problem. </div></div>Zoomの参加URLはこちらのGoogle formから申請して下さい。<br class=""><br class=""><a href="https://forms.gle/vSFPoVR6ugrkTGhX7" class="">https://forms.gle/vSFPoVR6ugrkTGhX7</a><br class=""><br class="">前回参加の方には参加URLをお送りしますので再度の申込みは不要です。<br class="">講演者も募集中です。<br class=""><br class="">世話人<br class="">平地 健吾, 高山 茂晴</div></body></html>