<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<div style="FONT-SIZE: small; TEXT-DECORATION: none; FONT-FAMILY:
"Calibri"; FONT-WEIGHT: normal; COLOR: #000000;
FONT-STYLE: normal; DISPLAY: inline">
<div style="FONT-SIZE: small; TEXT-DECORATION: none; FONT-FAMILY:
"Calibri"; FONT-WEIGHT: normal; COLOR: #000000;
FONT-STYLE: normal; DISPLAY: inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ; DISPLAY:
inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
幾何学分科会の皆様， </div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ; DISPLAY:
inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ; DISPLAY:
inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
<div style="TEXT-DECORATION: ; FONT-FAMILY: ; COLOR: ;
DISPLAY: inline">
</div>
</div>
</div>
</div>
</div>
</div>
<div dir="ltr">Workshop 「Geometric Analysis in Geometry and Topology 2018」（第2報）</div>
を下記の要領で開催いたしますのでご案内申し上げます．<br>
なお案内のPDF-file（英語版）とも，<br>
幾何学分科会のwebページに最新のものをおいていただくように致します．<br>
<br>
<div dir="ltr">多数のご参加をお待ち申し上げます．</div>
<div dir="ltr">またお近くの方にお声をかけて頂ければ幸いです．<br>
<br>
中央大学・理工学部<br>
芥川和雄<br>
<br>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<br>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\begin{document}</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\noindent </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf Date：}March 11th --\ 14th, 2019\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf Place：}Chuo University (Korakuen Campus) 6th building, 61125\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf Invited speakers} \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,{\bf Eric Bahuaud (Seattle University)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,{\bf Renato Bettiol (City University of New York)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,{\bf Boris Botvinnik (University of Oregon)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,{\bf Kei Irie (University of Tokyo)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Schedule}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
・・・・・・・・・・・ 10:00--11:00\qquad 11:30--12:30\qquad 14:00--15:00\qquad 15:30--16:30\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf March\,11}\quad B.\,Botvinnik-1\b\ B.\,Botvinnik-2\ \ R.\,Bettiol-1\quad \ \ R.\,Bettiol-2 \\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf March\,12}\quad E.\,Bahuaud-1\quad E.\,Bahuaud-2\quad B.\,Botvinnik-3\ \ B.\,Botvinnik-4\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf March\,13}\quad K.\,Irie-1\qquad \quad \ \ K.\,Irie-2 \qquad \quad {\bf Short Excursion} \\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf March\,14}\quad R.\,Bettiol-3\qquad R.\,Bettiol-4\qquad E.\,Bahuaud-3\quad E.\,Bahuaud-4 \\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
{\bf Organizers}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Shu Nakamura (University of Tokyo)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Mikio Furuta (University of Tokyo)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Shinichiroh Matsuo (Nagoya University)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Tsuyoshi Kato (Kyoto University)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Yoshihiko Matsumoto (Osaka University)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Nobuhiko Otoba (University of Regensburg)\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Rafe Mazzeo (Stanford University, Foreign adviser)\\</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\,Kazuo Akutagawa (Chuo University)\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
-----------------------------------------------\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\newpage\noindent</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\boxed{\bf Titles\ \&\ Abstracts\ of\ Lectures}$\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\ \ {\bf Eric Bahuaud (Seattle University, USA)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lectures 1--2\,:\,Poincar\'e-Einstein metrics with prescribed conformal infinity}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ The seminal work of Fefferman and Graham on conformal invariants introduced
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
an important existence problem: given a compact conformal manifold $(X, [g])$, is it possible to find a manifold with boundary $M$ with boundary$(M) = X$
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
and a conformally compact Einstein metric $g$ on the interior of $M$ that has $[g]$ as conformal infinity ?
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
In these talks I will introduce this problem and the explain the Graham-Lee theorem
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
that proves the existence of such metrics nearby the hyperbolic metric on the ball.
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
I will then discuss recent work with Lee on low regularity Poincar\'e-Einstein metrics.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lectures 3--4\,:\,Ricci flow of asymptotically hyperbolic metrics}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ In these two talks I'll survey results concerning the normalized Ricci flow evolving from a conformally compact asymptotically hyperbolic metric.
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
I'll discuss joint work with Mazzeo and Woolgar on the behavior of the renormalized volume along the flow of both asymptotically Poincar\'e-Einstein metrics
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
and metrics with an even expansion. </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
I'll then discuss joint work with Woolgar on the long-time existence of the flow for rotationally symmetric asymptotically hyperbolic initial data,
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
and ongoing work with Guenther and Isenberg on the stability of these flows.\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\ \ {\bf Renato Bettiol (City University of New York, USA)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lectures 1-- 4\,:\,Applications of Bifurcation Theory to Geometric Analysis}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lecture 1\,:\,Introduction to Bifurcation Theory}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ Bifurcation Theory originates from problems in Applied Sciences and Engineering (such as the buckling of columns under compressive stress),
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
and was developed by mathematicians into a powerful toolkit that uses the instability of solutions to certain problems to prove the existence of other solutions nearby.
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
These "bifurcating" solutions are often less symmetric and harder to find directly, but can provide very interesting examples.
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
In this first lecture, I will give a broad overview of bifurcation methods and some classical applications.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lecture 2\,:\,Bifurcating Constant Mean Curvature Hypersurfaces}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ In this second lecture, I will survey on applications of Bifurcation Theory to establish the existence of many hypersurfaces with Constant Mean Curvature.
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
In particular, I will describe a construction of Delaunay-type hypersurfaces in cohomogeneity one manifolds, which generalizes classical Delaunay surfaces.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lecture 3\,:\,Bifurcating solutions to the classical Yamabe problem}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ The third lecture will focus on proving the existence of infinitely many solutions to the (classical) Yamabe problem on certain closed manifolds,
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
that is, Riemannian metrics with constant scalar curvature in prescribed conformal classes. Key examples are products and total spaces of Riemannian submersions.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lecture 4: Bifurcating solutions to generalizations of the Yamabe problem}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
In this last lecture, I will describe how similar bifurcation techniques yield infinitely many solutions to certain generalizations of the Yamabe problem to noncompact manifolds,
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
as well as to higher order problems in conformal geometry, such as the fourth-order Q-curvature problem.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\newpage\noindent</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\ \ {\bf Boris Botvinnik (University of Oregon, USA)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Main topic\,:\,Spaces of psc-metrics and moduli spaces of psc-metrics}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lectures 1--3\,:\,The space of positive scalar curvature\,:\,constructions,} \\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf results and conjectures}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ \underline{Lecture 1}\ : Geometric constructions and results concerning the relevant</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
spaces of metrics, conformal classes and corresponding moduli spaces.</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
Surgery results, homotopy invariance of the space of psc-metrics under surgery.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{Lecture 2}\ : Dirac operator and psc-curvature, Gromov-Lawson-Stolz results;</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
concordance/isotopy, index theory for families of metrics. Hitchin's results.</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
Index theory and moduli spaces of metrics.\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{Lecture 3}\ : Spaces of smooth manifolds and of manifolds with psc-metrics.
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
Review of the results on the moduli spaces following Madse-Weiss, Galatious, Randal-Williams.\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lecture 4\,:\,Positive scalar curvature metrics on manifolds with fibered}\\
</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf singularities}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ Index-difference map and review of the results following Botvinnik--Ebert--Randal-Williams</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
on the homotopy type of the space of psc-metrics.\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
$\bullet$\ \ {\bf Kei Irie (University of Tokyo, Japan)}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\quad \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Lectures 1--2\,:\,Symplectic homology}\\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\underline{\bf Abstract}\ \ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
Symplectic homology was introduced by Floer-Hofer and Viterbo in early</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
nineties, combining two important ideas in symplectic geometry:</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
symplectic capacity and Floer homology. It is now one of standard tools</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
in symplectic topology and its applications to Hamiltonian dynamics.</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
The goal of my talks will be to outline the theory with a few sample</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
applications, such as a proof of Weinstein conjecture on periodic orbits</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
of Hamiltonian dynamics on symplectic vector spaces, and a proof of</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
Gromov non-squeezing theorem.</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
If time permits, I will discuss a few topics from recent research. \\ </p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px;
margin-right:0px; -qt-block-indent:0; text-indent:0px;">
\end{document}</p>
<br>
</div>
</body>
</html>