Xiao Wang (Cornell, Eun-Ah Kim group) introduces droplet dynamics — a compact spatial block of local excitations or defect insertions embedded in a much larger quantum background — and shows how it realizes a universal class of unconventional dynamical transitions, identified as dynamical Gross–Witten–Wadia transitions, in both the XX/free-fermion and transverse-field Ising chains.

The presentation argues that for modern physics research, the key question is no longer whether to use AI, but how to use it effectively. It distinguishes two major roles: NN-based AI for principles (neural-network fitting, neural quantum states, DeepH) and LLM-based AI for workflow (planning, memory, tools, APIs, MCP, agent loops).

These notes build the bulk–boundary correspondence of topological band insulators from the ground up — from the modern theory of polarization to the protected edge spectrum and the wider topological zoo. Both the typeset write-up and the original handwritten notes are attached below.

A survey of how topological insulators are actually made and measured: from the band-inversion picture and the 2D/3D material platforms that realize it, to the experimental probes — ARPES, molecular beam epitaxy, and STM/STS — that reveal and characterize the protected surface states.