# Subject: Critical nonlinear dispersive equations.

### Introduction

The participating school is an intensive reading seminar. The goal is to learn about important recent progress in analysis and PDE. We choose a subject which has shown great progress in recent years and select a series of breakthrough works for discussion. The organizers will give lectures providing background and context for these works.  Each participant will presents one topic in two lectures. The main target is graduate students and young researchers working in the area of analysis.  Experienced researchers who are interested in this topic are also welcome. The school is supported by CMC at KAIST

Dates:   July 20(Mon) ~ 24(Fri), 2015 (arrive on 19th, depart on 25th).

Location: KAIST, Daejeon, Korea.

### List of topics

1. R. Killip, S. Kwon, S. Shao, and M. Visan, On the mass-critical generalized KdV equation. Discrete Contin. Dyn. Syst. 32 (2012), no. 1, 191–221.  MR2837059
Presenter : Younghak Kwon(SNU), Junki Jeon(ETRI)

2. B. Dodson, Global well-posedness and scattering for the defocusing, mass-critical generalized KdV equation.  Preprint arXiv:1304.8025

Presenter : Heywon Yoon(KAIST), Sunghyun Hong(KAIST)

3. R. Killip, B. Stovall, and M. Visan, Scattering for the cubic Klein-Gordon equation in two space dimensions. Trans. Amer. Math. Soc. 364 (2012), no. 3, 1571–1631. MR2869186
(Sections 1-5.)

Presenter: Mamoru Okamoto(Shinshu University)

4. H. Herr, D. Tataru, and N. Tzvetkov, Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in $H^1(\T^3)$.Duke Math. J. 159 (2011), no. 2, 329–349. MR2824485       Presenter : Chulkwang Kwak(KAIST)

5. A. Ionescu and B. Pausader, The energy-critical defocusing NLS on $\T^3$. Duke Math. J. 161 (2012), no. 8,1581–1612.  MR2931275       Presenter : Hiroyuki Hirayama(Nagoya University)

6. M. Visan, Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. Int. Math. Res. Not. IMRN 2012, no. 5, 1037–1067.
MR28999597.
Presenter : Gyeongha Hwang(UNIST)
7. H. Jia and V. Sverak, Minimal $L^3$-initial data for potential Navier-Stokes singularities. SIAM J. Math. Anal. 45(2013), no. 3, 1448–1459. MR3056752
Presenter : Yifei Wu(Beijing Normal University)
9.  R. Killip and M. Visan, The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher. Amer. J. Math. 132 (2010), no. 2, 361–424. MR2654778
Presenter: Masaki Satoshi (Hiroshima University)
10. T. Tao, A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations. Dyn. Partial Differ. Equ. (2007), no. 1, 1–53. MR2304091
Presenter: Younghun Hong(U Texas,Austin)

Lecture room : E6-1, Room 1409    map

Accommodation : Daeduk innopolis geust house

### Schedule

 Mon Tue Wed Thr Fri 11:00-11:50 Killip Killip Killip Y Hong Kwak Lunch 2:00-2:50 Killip Killip Y Kwon S Hong Y Hong 3:00-3:50 Jeon Wu Kwak Wu Yoon Hwang Hwang
Registration

Space is limited. As we will discuss 10 topics this year, we expect at most 10~16 spaces will be available. Typical participants will be graduate students, postdocs, or young researchers working in or near the field. They need not be experts in the subject. If you are interested in participating, please write a short email to Soonsik Kwon <soonsikk@kaist.edu> as soon as possible, but no later than Apr 30. In your email, describe your academic status, field of interest, and motivation to participate.  If you have a Ph.D., attach your CV; if you are a graduate student, then have your advisor write a short email on your dissertation topic.  You may also indicate which among the 10 papers you would prefer to present.  CMC supports local expenses including accommodation and meals for all participants. However, we ask participants to fund their travel from other sources.

### Instruction to participants

Each participant will give two talks on a single paper, each of 50 min. Blackboard presentations are preferred and participants are encouraged to practice/time their talks before arriving at the meeting.  Organizers will assign topics to present to each participant, according to their preference list. Participants are expected to submit a summary of their talk at least two weeks prior to the meeting. Printouts of the summaries will be available at the meeting. We highly recommend participants to familiarize themselves with the content of most articles in the list before the meeting. If you don’t have access to any of the papers in the list from your affiliation, the organizers can provide PDF files; note that most are freely available on the arXiv.