My research interests lie in developing and applying tools from Markov chain theory, dynamical systems, geometric measure theory, and the calculus of variations to problems in machine learning and in physics. My research focuses on deriving asymptotic results for stochastic gradient descent Markov chains and analyzing regularizations of the classical model for charged fluid droplets.
Publications
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D. Shirokoff and P. Zaleski. Convergence of Markov chains for constant step-size
stochastic gradient descent with separable functions. SIAM J. Appl. Dyn.
Syst., 24(3), 2025.
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C. B. Muratov, M. Novaga, and P. Zaleski. A variational model of charged
drops in dielectrically matched binary fluids: the effect of charge discreteness.
Arch. Ration. Mech. Anal., 248(76), 2024.
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M. Lee, A. Shelke, S. Singh, J. Fan, P. Zaleski, and S. Afkhami. Numerical
simulation of superparamagnetic nanoparticle motion in blood vessels for magnetic
drug delivery. Phys. Rev. E, 106(1), 2022.
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J. Zaleski, P. Zaleski, and Y. V. Lvov. Excitation of interfacial waves via
surface–interfacial wave interactions. J. Fluid Mech., 887(14), 2020.
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P. Zaleski and S. Afkhami. Dynamics of an ellipse-shaped meniscus on a
substrate-supported drop under an electric field. Fluids, 4(4), 2019.
For more information see my Google Scholar.
CV
For a overview of my research, teaching, and publications, please see my CV.