강경근 (연세대학교) / kang@yonsei.ac.kr

Title: Singular gradients of solutions for the Stokes system and Navier-Stokes equations near boundary in the half-space

Abstract: We study local regularity of the solutions for the Stokes system and Navier-Stokes equations
near boundary in the hlaf-space. Due to a non-local eect, in general, smoothness may not
be expected locally near boundary. Unlike interior case, in particular, regularity for spatial
variables is not true for the boundary case. The results addressed in this talk are joint works
partly T.-K. Chang and partly with B. Lai, C.-C. Lai, and T.-P. Tsai.
 

강문진 (KAIST) / 

tba

고동남 (가톨릭대학교) / ongnamko@catholic.ac.kr

Title: On the stochastic synchronization of the Winfree model with a multiplicative noise

Abstract: We focus on the stochastic convergence of the Winfree oscillators under multiplicative
noise. The long-time behaviors of the density prole mainly follows the Fokker-Planck equa-
tions, where the multiplicative noise commonly makes accumulation of density, which indicates
collective behaviors of stochastic oscillators. In this talk, we use a stochastic version of the
Barbalat's lemma to prove it in the level of particle dynamics (SDE). We mainly consider the
gradient ow with multiplicative noise to conclude stochastic convergence in almost-sure sense.
This analysis can be directly applied to other dynamics, such as the Kuramoto model. This is
a joint work with Seung-Yeal Ha from SNU and Woojoo Shim from KIAS.
 

고동영 (Rutgers University) / dongyeong.ko@rutgers.edu

Title: Morse Index of simple closed geodesics on Riemannian 2-sphere

Abstract: In this talk, we introduce results on the Morse-theoretic characterization of simple closed
geodesics on Riemannian 2-sphere. More specically, there are simple closed geodesics with
Morse index 1, 2 and 3 on a generic 2-sphere (S2; g). This conjectural bound is optimal by the
example of triaxial ellipsoids of Morse. This is the simple closed geodesic on 2-sphere version
of Marques-Neves Morse theory for the area functional.

김건우 (POSTECH) / kunwoo@postech.ac.kr

Title: The compact support property for stochastic heat equations

Abstract: In this talk, we consider the compact support property for the following stochastic heat
equations:

                                                     
where  > 0 is a xed constant and  = (t; x) is Gaussian noise, which is white in time and
colored in space. Here, the compact support property (CSP) refers to the property that if the
initial function has compact support, then so does the solution for all time t > 0. In other
words, CSP means the nite speed of propagation. We show that, under some mild condition
on the noise that guarantees the existence and continuity of the solution, CSP holds with
probability one if and only if  2 (0; 1). This is based on joint work with Beom-Seok Han and
Jaeyun Yi.

김경윤 (National Chung Hsing University) / kyungyoun07@gmail.com

Title: Heat kernel estimates for a large class of anisotropic Markov Process

Abstract: We consider a d-dimensional pure jump Markov process M with a jumping kernel compara-
ble to a d-dimensional anisotropic Levy process L, where the coordinates of L are independent
1-dimensional Levy processes. We obtain the sharp two-sided bounds of the fundamental solu-
tion(heat kernel) for the non-local operators corresponding to the pure jump Markov processes
M. This talk is based on two projects: a joint work with Moritz Kassmann and Takashi Ku-
magai and a joint work with Lidan Wang. The rst is a study of the Markov process where
each coordinate is comparable to the -stable process, and the second is a study of the general
Markov process in which the Levy kernel has the weakly scaling condition. 

김준하 (KIAS) / junha02@kias.re.kr

Title: Asymptotic Stability of the Inviscid Incompressible Porous Medium Equation

Abstract: We consider the IPM equation:

                                                      
where u is the velocity eld of the uid, p is the pressure, and  is the liquid density. It was
proved by Tarek M. Elgindi that the stratied state (us; s; ps) := (0; x2; 1
2x22) is asymptotically
stable in the domains R2 and T2. In this talk, we provide a neighborhood of (us; s; ps)
consisting of stationary solutions to the IPM equation, where all elements are asymptotically
stable. In particular, this is an improvement over the previous stability results.

김판기 (서울대학교) / pkim@snu.ac.kr

Title: Positive self-similar Markov processes obtained by resurrection

Abstract: A [0;1)-valued standard Markov process X = (Xt; Px), t  0, x  0, is called a positive
self-similar Markov process(pssMp) if there exists  > 0 such that for any x > 0 and c > 0,
the law of (cXc