On June 23, 2026, Prof. Junyong Zhang from the School of Mathematics and Statistics, Beijing Institute of Technology delivered an invited academic lecture titled“Some harmonic analysis results for two types of conical singular Schrödingeroperators and applications”. Faculty and graduate students majoring in partial differential equations, harmonic analysis and geometric analysis attended the seminar.In the lecture, Zhang Junyong pointed out that harmonic analysis, as a fundamental tool for partial differential equations, has developed a mature theory in Euclidean space. However, conical singular manifolds render classical Fourieranalysis inapplicable due to vertex singularities, and Schrödinger operators withelectromagnetic potentials remain a long-standing challenge because the magnetic field term destroys conventional perturbation methods. Current research bottlenecksmainly lie in the unresolved product cone dispersive estimate conjecture and the lack of pseudo-conformal invariance for wave and Klein–Gordon equations in two-dimensional electromagnetic potentials, which creates gaps in space-time decay estimates. To address these challenges, his team conducted systematic research on conical singular manifolds and critical electromagnetic potentials, achieving three progressive results: they refined the dispersive estimate theory on cones, partially resolving the product cone conjecture and filling the gap for wave equations in two-dimensional electromagnetic potentials; they established a weighted resolvent estimate framework for critical electromagnetic Schrödinger operators, providing criteria for magnetic flux; and they ultimately constructed a unified analytical framework for potential-perturbed dispersive equations, clarifying the effects of different potential fields and offering theoretical support for subsequent studies such as nonlinear scattering.After the main talk, participants raised questions focusing on geometricrestrictions of product cones and critical threshold of magnetic flux in 2D. The event concluded successfully amid warm applause.（By Yifei Wu）