Time: Mar 21 (Fri) 11:00-12:00 AM
Speaker: 성기훈 (Kihoon Seong) (Cornell University)
Title: Central limit theorem for Φ^4 QFT measures in low temperature and the thermodynamic limit
Abstract: I will introduce basic concepts such as the concentration and fluctuation of Φ^4 Gibbs type measures from the perspectives of statistical physics, quantum field theory, probability theory, and PDEs. The focus will be on the low temperature behavior and the thermodynamic limit of these probability measures, with particular attention to fluctuations around the soliton manifold.
This talk is intended for general (PDE) audiences and does not require a background in probability theory
Time: Apr 11 (Thu) 4:00-5:00 PM
Speaker: Miguel Alejo (Universidad de Cordoba)
Title: On the nonexistence of NLS breathers
Abstract: In this talk, we will show a proof of the nonexistence of breather solutions for NLS equations. By using a suitable virial functional, we are able to characterize the nonexistence of breather solutions by only using their inner energy and the power of the corresponding nonlinearity of the equation. We extend this result for several NLS models with different power nonlinearities and even the derivative NLS equation.
Time: May 29 (Thu) 5:00-6:00 PM
Speaker: Kouichi Taira (Kyushu University)
Title: Dispersive estimates for Schrödinger equations on conic manifolds
Abstract: In this talk, I will introduce my results on time decay estimates for Schrödinger equations, known as dispersive estimates, on manifolds with conical singularities. In Euclidean space, the $L^1$–$L^{\infty}$ norm of the Schrödinger propagator has a singularity at time zero and decays as time grows. On conic manifolds, such estimates may fail due to a conical singularity of the potential or the presence of conjugate points. The proof relies entirely on tools from harmonic analysis, such as the stationary phase method.
Time: Jun 12 (Thu) 4:00-5:00 PM
Speaker: Jiawei Cheng (Fudan University)
Title: Decay estimates for dispersive equations on the lattice graph
Abstract: In this talk, I will show a method to get time decay rates for the fundamental solutions of dispersive equations on the discrete graph Z^d. As in the setting of Euclidean space, it is necessary to deal with the asymptotic behaviour of oscillatory integral with parameters. Newton polyhedra and an algorithm dated back to Karpushkin will be introduced as two important parts in the proof. In a more general sense, our method will focus on obtaining uniform decay estimate for highly degenerate oscillatory integrals.
Time: Jun 30 (Mon) 4:00-5:00 PM
Speaker: Kenjiro Ishizuka (Kyoto University)
Title: Long-time asymptotics of 3-solitary waves for the damped nonlinear Klein-Gordon equation
Abstract: We consider the damped nonlinear Klein-Gordon equation. For the damped nonlinear Klein-Gordon equation, there are several studies on the long-time asymptotics of the multi-solitary waves. Cote, Martel, Yuan, and Zhao proved that 2-solitary waves with the same sign does not exist and that 2-solitary waves with opposite sign behaves as if the two solitons are on a line. In this talk, I prove that 3-solitary waves behaves as if the three solitons are on a line, and it has alternative signs.