| 講演タイトル，アブストラクト：
abstract
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| Yng-Ing Lee （National Taiwan Univ., Taiwan) |
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Title: "Special solutions to Lagrangian Mean Curvature Flow"
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Abstract: Mean curvature flow deforms a submanifold in the direction of its mean curvature vector.
When the initial submanifold is Lagrangian in a Kahler-Einstein manifold,
the solution will continue
to be Lagrangian whenever it is smooth. It thus becomes a nice way to construct special
Lagrangians.
However, finite-time singularities may occur in general and cause the main difficulties.
I will report some of my works with a few collaborators on special solutions to Lagrangian mean
curvature flow that is closely related to the study of singularities.
Most of the talk will concentrate on examples related to Schoen-Wolfson cones, which are the
obstructions to the existence of special Lagranians in two-dimension.
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| Su-Jen Kan（Academic Sinica, Taiwan) |
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Title: "Complete Ricci-flat metrics through a rescaled exhaustion" |
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Abstract:
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| Tai-Chia Lin （National Taiwan Univ., Taiwan) |
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Title: "The Poisson-Nernst-Planck system for ion transport"
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Abstract: Understanding ion transport is crucial in the study of many physical and biological problems, such as semiconductors, electro-kinetic fluids, transport of electrochemical systems and ion channels in cell membranes. One of the fundamental models for the ionic transport is the time dependent coupled diffusion-convection equations, the Poisson-Nernst-Planck (PNP) system. The PNP system consists of the electro-static Poisson and Nernst-Planck equations describing electro-diffusion and electrophoresis. In this lecture, I’ll introduce our recent results on the equilibrium of the PNP system and the linear stability problem.
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| Chiung-Ju Liu（National Taiwan Univ., Taiwan) |
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Title: "Bergman kernel on singular Riemann surfaces" |
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Abstract:
The Bergman kernel has a asymptotic expansions on smooth polarized compact Kahler manifolds. However, some properties may not hold on singular manifolds. In this talk, we will study the information of the singularity in the expansion.
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| Wu-yen Chuang（National Taiwan Univ., Taiwan) |
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Title: "Wallcrossing in ADHM theory and Cohomology of the Hitchin system" |
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Abstract:
I will introduce ADHM sheaf theory and present a conjectural
recursive formula for the Poincare/Hodge polynomial of Hitchin
system. The formula is derived from the wallcrossing of ADHM
sheaf theory on curves. It establishes a connection between
previous work of Hausel and Rodriguez-Villegas and refined
local Donaldson-Thomas invariants.
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| Ting-Hui Chang (Academic Sinica, Taiwan) |
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Title: "On the existence of pseudoharmonic maps from pseudohermitian manifolds into
Riemannian manifolds with nonpositive sectional curvature" |
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Abstract:
In this talk, we first derive a CR Bochner identity for the pseudoharmonic map heat flow
on pseudohermitian manifolds. Secondly, we are able to prove the existence of global
smooth solution for the pseudoharmonic map heat flow from a closed pseudohermitian
manifold into a Riemannian manifold with nonpositive sectional curvature.
In particular, we prove the existence theorem of pseudoharmonic maps.
This is served as the CR analogue of Eells-Sampson's Theorem for the harmonic map heat
flow.
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| Kuo-Wei Lee (Academic Sinica, Taiwan) |
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Title: "The mean curvature flow of compact submanifolds in higher codimension" |
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Abstract:
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| Mikiya Masuda（Osaka City Univ., Japan) |
| Title: "Iterated circle bundles" |
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Abstract:
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| Qing-Ming Cheng（Saga Univ., Japan) |
| Title:
"Estimates for eigenvalues on complete Riemannian manifolds" |
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Abstract:
In this talk, we consider the Dirichlet eigenvalue problem
of the Laplacian on a bounded domain in complete Riemannian
manifolds. Estimates for eigenvalues will be discussed. We will talk
about the conjecture of Polya for the lower bounds for eigenvalues
on a bounded domain in Euclidean spaces and the generalized
conjecture of Polya for the lower bounds of eigenvalues on a bounded
domain in complete Riemannian manifolds. In order to obtain
the lower bounds of eigenvalues, we need to have sharper universal
inequalities for eigenvalues and the recursion formula of Cheng
and Yang (Math. Ann. 2007). Furthermore, we will deal with
the upper bounds for eigenvalues. In particular, for lower order
eigenvalues, we will discuss the conjectures of Payne, Polya and
Weinberger and their generalizations.
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| Ryushi Goto（Osaka Univ., Japan) |
| Title:
"Holomorphic Poisson and generalized Kahler structures" |
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Abstract:
First I will give a brief introduction of generalized complex and
generalized Kaehler geometry.
Deformations of generalized complex and generalized Kahler structures are disc
ussed.
Holomorphic Poisson structures gives rise to intriguing generalized Kaehler
structures.
Next I will construct Ricci-flat conical Kaehler metrics on crepant
resolutions of Sasaki-Einstein cones in every Kaehler class.
Applying the deformation method by Poisson structures in generalized geometry,
I will deform ordinary Calabi-Yau structures to obtain generalized Calabi-Yau metrical
structures on the crepant resolution.
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| Yasuyuki Nagatomo（Kyushu Univ., Japan) |
| Title: "Harmonic maps into Grassmannians and its applications
to isoparametric functions and moduli problems" |
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Abstract:
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| Yoshie Sugiyama （Tsuda College, Japan) |
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Title: "Measure valued solutions of the 2D Keller-Segel system" |
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Abstract:
We deal with the two-dimensional Keller-Segel system describing chemotaxis in a bounded
domain with smooth boundary under the nonnegative initial data. As for the Keller-Segel
system, the $L^1$ norm is the scaling invariant one for the initial data, and so if the
initial data is sufficiently small in $L^1$, then the solution exists globally in time.
On the other hand, if its $L^1$ norm is large, then the solution blows up in a finite time.
The first purpose of my talk is to construct a time global solution as a measure valued function
beyond the blow-up time even though the initial data is large in $L^1$.
The second purpose is to show the existence of two measure valued solutions of the
different type depending on the approximation, while the classical solution is unique
before the blow-up time.
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| Yohei Sato（OCAM I, Japan) |
| Title:"The existence and non-existence of positive solutions for the nonlinear Schroedinger equations" |
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Abstract:
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| Kensuke Onda （Nagoya Univ. & OCAM I, Japan) |
| Title:
"Sol-solitons on Lorentzian manifolds" |
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Abstract:
J. Lauret introduced Sol-soliton and studied in the Riemannian
framework.
Sol-solitons have relevance to Ricci solitons, that is fixed point of
the Ricci flow.
We study sol-soliton theory and use it to give sol-solitons and Ricci
solitons on Lorentzian manifolds.
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| Yohsuke Imagi （D1, Kyoto Univ., Japan) |
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Title: "A Uniqueness Theorem for Gluing Special Lagrangian Submanifolds" |
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Abstract:
Butscher, D. Lee, Y. Lee, and Joyce constructed a special
Lagrangian submanifold by gluing a Lawlor neck into a transverse
intersection point of two special Lagrangian submanifolds. I talk about
a uniqueness theorem for the gluing of flat special Lagrangian tori of
real dimension 3 in a flat complex torus of complex dimension 3.
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| Saki Okuhara （D1, Tokyo Metropolitan Univ., Japan) |
| "Special Lagrangian 3-folds via harmonic maps" |
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Abstract:
Special Lagrangian cones in ${\mathbb{C}}^3$ can be constructed
from certain harmonic maps into a 6-symmetric space.
We will review this process which was derived by Joyce and McIntosh,
and use it to give a new construction of special Lagrangian cones in
${\mathbb{C}}^3$.
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| Hitoshi Yamanaka（D2, Osaka City Univ., Japan) |
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Title: "Intersection of stable and unstable manifolds for invariant Morse functions" |
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Abstract:
In Witten's Morse theory, it is important to consider the negative gradient flows
which connect two critical points whose Morse indices differ by 1.
However there are too many examples of Morse functions which have no such pairs of critical points.
In the case of an invariant Morse-Smale function, we investigate the intersection of a
stable and an unstable manifold which corresponds to a pair of critical points
whose Morse indices differ by 2. We also consider the group action on it.
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