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I am interested in a wide range of topics related to applied mathematics, and I am always exploring new math problems during my research. Currently my interests are around:
Sampling
Markov chain Monte Carlo (MCMC)
Glauber Dynamics (optimal mixing time and its implications for modern machine learning)
Stochastic Localization (the theory framework for analyzing MCMC, and its implication for sampling and machine learning)
Optimal transport (the theory (Diffusions, Gradient Flow), and its applcation in machine learning)
Computation
Large-scale Matrix (tensor) Problem (especially randomized algorithm for the least-squares, eigenvalue problems)
Random Matrix theory (theoretical guarantee for structured random matrix)
My goals have been about two part
Develop theoretical insights in computational science that can more practically inform algorithmic design and implementation.
Explore new paradigms for the development of AI, enlightened by applied math/physics.
e-mail: ruihanx@uchicago.edu
More about Ruihan:
lifelong leaner, interest driven
doing sports is part of my life, bouldering recently, basketball before (I still can dunk)
amateur pianist, music making
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