Speaker: Jiawei Cheng (Fudan University)
Time: September 5, 2025, 2:00 p.m.
Location:R810, SIMIS
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. In particular, I will use the fourth-order Schrödinger equation as an example.
About speaker:
Jiawei Cheng is a phd at Fudan University, supervised by Professor Bobo Hua. His research focuses on dispersion equations on graphs (dispersion estimation, Strichartz estimation, and continuum limits). He is currently a joint student at Paris-Saclay University in France, with his international supervisor Nicolas Burq.
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