Recently, from the identification of matrix integral and the gravitational path integral, we had a significant progress in our understanding of non-perturbative correspondence between bulk geometry and the boundary quantum state. In this talk, we will explain aspects of such mapping between black hole interior geometry and the boundary quantum state, constructing "length operator" in the boundary theory. Using such operator, we confirm the Susskind's conjecture that the late time two sided BH is equal superposition of black holes and white holes. Furthermore, this program can be extended to the ETH matrix model for double-scaled SYK model, whose gravity dual has discrete structure, where we can see a connection to the Krylov complexity and its generalizations.
Biography：
Masamichi Miyaji is a senior research scientist at RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences. He received his PhD from Kyoto university in 2019, M.S. from Kyoto university in 2016, and B.S. from Kyoto university in 2014. Before joining Riken in 2025, he was an assistant professor at Yukawa institute for theoretical physics and Nagoya university. His research focus on quantum gravity, black hole, and quantum universe.
Shanming Ruan