Explore a 39-minute conference talk on improved complexity estimation for Hamiltonian simulation using the Trotter formula. Delve into Dong An's presentation at IPAM's Quantum Numerical Linear Algebra Workshop, covering two specific scenarios: simulating the Schrödinger equation with time-dependent effective mass and near adiabatic dynamics. Discover how measuring error in vector norm can potentially reduce computational costs, and learn about the efficiency of first-order Trotter formula in discrete near adiabatic evolution operators. Gain insights into the poly-logarithmic scaling of complexity under certain conditions and understand the implications for quantum numerical linear algebra.