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publications
The Mattig Expression for a d-dimensional Gauss Bonnet FRWL Cosmology
Published in arXiv, 2016
We study the form of the Mattig equation applied in a cosmological setting for spacetime metric gravity models described by the Gauss-Bonnet action.
Recommended citation: Andrew, Keith; Steinfelds, Eric; Zolman, Nick. (2016). "The Mattig Expression for a d-dimensional Gauss Bonnet FRWL Cosmology." arXiv preprint. https://arxiv.org/abs/1601.07037
The Origin and Evolution of the Galaxy Mass–Metallicity Relation
Published in Monthly Notices of the Royal Astronomical Society, 2016
We use high-resolution cosmological zoom-in simulations from the Feedback in Realistic Environment (FIRE) project to study the galaxy mass–metallicity relations (MZR) from z = 0–6.
Recommended citation: Xiangcheng Ma, Philip F. Hopkins, Claude-André Faucher-Giguère, Nick Zolman, Alexander L. Muratov, Dušan Kereš, Eliot Quataert, The origin and evolution of the galaxy mass–metallicity relation, Monthly Notices of the Royal Astronomical Society, Volume 456, Issue 2, 21 February 2016, Pages 2140–2156, https://doi.org/10.1093/mnras/stv2659 https://academic.oup.com/mnras/article/456/2/2140/1061514?login=true
Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples
Published in p-Adic Numbers, Ultrametric Analysis and Applications, 2019
We investigate the spectral geometry and spectral action functionals associated to 1D Supersymmetry Algebras.
Recommended citation: Marcolli, M., Zolman, N. Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples. P-Adic Num Ultrametr Anal Appl 11, 223–247 (2019). https://doi.org/10.1134/S2070046619030051 https://link.springer.com/article/10.1134/S2070046619030051
Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution
Published in Aerospace, 2023
Using Hamiltonian and mathematical priors, we infer the dynamics of a rotating rigid body from images with no access to ground-truth information.
Recommended citation: Mason, J. J., Allen-Blanchette, C., Zolman, N., Davison, E., & Leonard, N. E. (2023). Learning to predict 3D rotational dynamics from images of a rigid body with unknown mass distribution. Aerospace, 10(11), 921. https://www.mdpi.com/2226-4310/10/11/921
A unified framework to enforce, discover, and promote symmetry in machine learning
Published in arXiv, 2023
We provide the mathematical theory of how to enforce, discover, and promote symmetry in machine learning and optimization problems.
Recommended citation: Otto, Samuel E., et al. "A unified framework to enforce, discover, and promote symmetry in machine learning." arXiv preprint arXiv:2311.00212 (2023). https://arxiv.org/abs/2311.00212
SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning
Published in arXiv, 2024
We develop unifying methods for incorporating sparse dictionary learning into RL algorithms to accelerate the training process and provide more interpretable representations of the environment dynamics, reward, and policy.
Recommended citation: Zolman, Nicholas, et al. "SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning." arXiv preprint arXiv:2403.09110 (2024). https://arxiv.org/abs/2403.09110
teaching
Ordinary Differential Equations
Undergraduate course, UCLA, Department of Mathematics, 2017
Math 33B: UCLA’s introductory course to ordinary differential equations. Focusing primarily on application and techniques for soliving first and second order differential eqautions.
Linear and Nonlinear Systems of Differential Equations
Upper divison undergraduate course, UCLA, Department of Mathematics, 2018
Math 134: UCLA’s upper division course introducing applied dynamical systems theory. The course followed Strogatz’s text, covering the basics of nonlinear dynamics theory and bifurcations.
Introduction to Complex Analysis
Upper divison undergraduate course, UCLA, Department of Mathematics, 2018
Math 132: UCLA’s upper division course for complex analysis with an emphasis on applications to engineering and the applied sciences. Covered complex variables and arithmetic, complex analytic and harmonic functions, branch cuts, contour integrals, Cauchy-Riemmann equaions, Laurent series, and the residue theorem.