PhD Comprehensive Exam | Yun Su, Developing Data-Driven Neural Network Approaches for Solving High-Dimensional Hamilton-Jacobi-Bellman Equations
MC 5501
MC 5501
MC 5501
MC 5501
MC 5501
MC 6460
M3 4206
M3 4206
Mengyao Zhang | Applied Mathematics, University of Waterloo
On Convergence Analysis of Stochastic and Distributed Gradient-Based Algorithms
This research proposal explores the role of Poisson-Lie and quantum group symmetries in gravity and physics. We review the previously established appearances of Poisson-Lie symmetries (the semi-classical picture of quantum group symmetries) and quantum group symmetries in 3D gravity as well as our novel advancements in elucidating such structures in 4D gravity.
General Relativity is currently the most successful theory for our understanding of gravity and spacetime. Proposed by Albert Einstein more than 100 years ago, its predictions are still being proven accurate by cutting-edge experiments, exemplified by the detection of gravitational waves by LIGO in 2015 and the black hole picture obtained in 2022. However, there still is much to be understood when Quantum Physics comes into play. For years, many physicists have tried to obtain a complete theory of Quantum Gravity, but we still do not have one.