Ari Stern

Assistant Professor of Mathematics, Washington University in St. Louis

About Me

I received my B.A. and M.A. from the mathematics department at Columbia University. In 2009, I completed my Ph.D. in Applied and Computational Mathematics at Caltech, under the direction of the late Jerrold E. Marsden and Mathieu Desbrun. Before arriving at Wash. U. in 2012, I was a postdoc in the mathematics department at UCSD, where I worked with Michael Holst.

Teaching

Fall 2014: Math 449, Numerical Applied Mathematics.

Previous Courses

Spring 2014: Math 515, Partial Differential Equations.
Fall 2013: Math 456, Topics in Financial Mathematics.
Spring 2013: Math 5052, Measure Theory and Functional Analysis II.
Fall 2012: Math 5051, Measure Theory and Functional Analysis I.

Research Interests

My research lies at the intersection of geometry, applied analysis, and computational mathematics. I am interested in what I call geometric numerical analysis: using geometry as a means to develop novel numerical methods and techniques to analyze them. The driving idea behind this work is the need for numerical methods for differential equations that are accurate globally, not just locally—and, in recent years, it has been shown that these global features have important (and often surprising) connections with modern geometry, particularly differential and symplectic geometry.

Papers Available for Download

 
Marrero, J. C., D. Martín de Diego, and A. Stern (2015), Symplectic groupoids and discrete constrained Lagrangian mechanics. Discrete Contin. Dyn. Syst., 35 (1). In press. [ bib | arXiv ]
 
Leopardi, P., and A. Stern (2014), The abstract Hodge-Dirac operator and its stable discretization. Preprint. [ bib | arXiv ]
 
McLachlan, R. I., and A. Stern (2014), Modified trigonometric integrators. SIAM J. Numer. Anal., 52 (3), 1378-1397. [ bib | doi | arXiv ]
 
Stern, A. (2014), Banach space projections and Petrov-Galerkin estimates. Numer. Math.bib | doi | arXiv ]
 
Stern, A., Y. Tong, M. Desbrun, and J. E. Marsden (2014), Geometric computational electrodynamics with variational integrators and discrete differential forms. Geometry, mechanics, and dynamics: the legacy of Jerry Marsden, Fields Inst. Commun., Springer. In press. [ bib | arXiv ]
 
Norton, R. A., D. I. McLaren, G. R. W. Quispel, A. Stern, and A. Zanna (2013), Projection methods and discrete gradient methods for preserving first integrals of ODEs. Preprint. [ bib | arXiv ]
 
Stern, A. (2013), Lp change of variables inequalities on manifolds. Math. Inequal. Appl., 16 (1), 55-67. [ bib | doi | arXiv ]
 
Holst, M., and A. Stern (2012), Semilinear mixed problems on Hilbert complexes and their numerical approximation. Found. Comput. Math., 12 (3), 363-387. [ bib | doi | arXiv ]
 
Holst, M., and A. Stern (2012), Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces. Found. Comput. Math., 12 (3), 263-293. [ bib | doi | arXiv ]
 
Stern, A. (2010), Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids. J. Symplectic Geom., 8 (2), 225-238. [ bib | arXiv ]
 
Stern, A., and E. Grinspun (2009), Implicit-explicit variational integration of highly oscillatory problems. Multiscale Model. Simul., 7 (4), 1779-1794. [ bib | doi | arXiv ]
 
Stern, A. (2009), Geometric discretization of Lagrangian mechanics and field theories. Ph.D. thesis, California Institute of Technology. [ bib | http ]
 
Stern, A., Y. Tong, M. Desbrun, and J. E. Marsden (2008), Variational integrators for Maxwell's equations with sources. PIERS Online, 4 (7), 711-715. [ bib | doi | arXiv ]
 
Stern, A., and M. Desbrun (2006), Discrete geometric mechanics for variational time integrators. In SIGGRAPH '06: ACM SIGGRAPH 2006 Courses, pages 75-80, ACM Press, New York. [ bib | doi ]

Contact

Ari Stern
Department of Mathematics
Washington University in St. Louis
Campus Box 1146
One Brookings Drive
St. Louis, MO 63130-4889
Email: astern@math.wustl.edu

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