2013 Participating School in Analysis of PDE

Global theory of nonlinear dispersive equations.

Hideo Takaoka(Hokkaido University)

Introduction

Parcitipating school is an intensive reading seminar. The goal is to learn important recent progress in analysis and PDE. We choose a subject which have  shown great progress in recent years, select a series of breakthrough works in the subject. In the meeting each participant presents one of topics and discuss. Main target is graduate students and young researchers working in the area of analysis. But, experienced researchers who are interested in jointly learning are welcome. The school is supported by KMRS at KAIST.

Date:   Aug 26(Mon) ~ 30(Fri), 2013.

Participants will arrive at the venue on 25th(Sun) and leave on 30th or 31st.

Location: Unipark(Jeju National University Park), Seogwipo, Jeju island, Korea.

List of topics

1. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., and Tao, T., \emph{Sharp global well-posedness for KdV and modified KdV on $\mathbb{R}$ and $\mathbb{T}$ }, J. Amer. Math. Soc, 16(3), 705-749. presenter: Yifie Wu note
2. Colliander, J., Tzirakis, N., and Grillakis, M. G., \emph{Tensor products and correlation estimates with applications to nonlinear Schrödinger equations}, Communications on pure and applied mathematics, 62(7), 920-968. presenter: Takamori Kato slide
3. Bourgain, J., \emph{Approximation of solutions of the cubic nonlinear Schrödinger equations by finite-dimensional equations and nonsqueezing properties}, International Mathematics Research Notices, 1994(2), 79-90. presenter: Gyeongha Hwang slide
4. Bourgain, J., \emph{Periodic nonlinear Schrödinger equation and invariant measures}, Communications in Mathematical Physics, 166(1), 1-26. presenter: Mamoru Okamoto slide
5. Germain, P., Masmoudi, N., and Shatah, J., \emph{Global solutions for 3D quadratic Schrödinger equations}, International Mathematics Research Notices, 2009(3), 414-432. presenter: Hyewon Yoon slide
6. Weinstein, M. I., \emph{Lyapunov stability of ground states of nonlinear dispersive evolution equations}, Communications on Pure and Applied Mathematics, 39(1), 51-67. presenter: Bongsuk Kwon slide
7. Burq, N., Gérard, P., and Tzetkov, N., \emph{Two singular dynamics of the nonlinear Schrödinger equation on a plane domain}, Geometric And Functional Analysis, 13(1), 1-19. presenter: Yohei Yamazaki note
8. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., and Tao, T., \emph{Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation}, Inventiones mathematicae, 181(1), 39-113. presenter: Sunghyun Hong, Chulkwnag Kwak slide slide
9.  Babin, A. V., Ilyin, A. A., and Titi, E. S., \emph{On the regularization mechanism for the periodic Korteweg–de Vries equation}, Communications on Pure and Applied Mathematics, 64(5), 591-648. presenter: Hiroyuki Hirayama, Kotaro Tsugawa slide slide
10.  Keel, M., and Tao, T., \emph{Endpoint strichartz estimates}, American Journal of Mathematics, 955-980. presenter: Nobu Kishimoto slide

Registration

Space is limited. As we will discuss 10 topics this year, we expect slightly more than 10 spaces are available.
Typical participants will be graduate students, postdoc, or young researchers working near the field. They need not be expertised in the subject. If you are interested in participation, please write a short email to Soonsik Kwon soonsikk@kaist.edu by Mar 31. In your email, describe your academic status, field of interest, and motivation to participate. Also, please indicate your preferred topics to present (3~5 topics).

KMRS supports local expense including accommodation and meals for all participants. However, we ask participants to arrange their travel grant from other sources.

Instruction to participants

Each participant will give two talks of length 50 min on a single paper. Organizers will assign topics(=paper) to present to each participant, according to their preference list. Participants will submit a summary note if you will give blackboard talk or  slide file, if you will give slide talk, by two weeks before the meeting.
In the meeting, we will hand out a printout of notes and slides. We highly recommend participants to take a look at most of articles in the list before the meeting and bring them to the meeting. If you don’t have access to any of those papers in the list from your affiliation, then please ask organizers.