Alexander Vladimirsky

Condensed Timeline

Born in Odessa (USSR) in 1973.
Immigrated to USA in February 1991.
B.A. in Applied Mathematics from UC Berkeley in 1995.
Became a US citizen in August 1997.
Ph.D. in Applied Mathematics from UC Berkeley in 2001.
H.C.Wang Assistant Professor / NSF Postdoctoral Fellow at Cornell in 2001-2004.
Assistant Professor of Mathematics at Cornell in 2004-2010.

Member of graduate programs in Mathematics, Applied Mathematics, Theoretical & Applied Mechanics, Computational Science & Engineering.
Co-organizer (together with David Bindel) of the Scientific Computing and Numerics (SCAN) Seminar.
Co-organizer of the Cornell Mathematical Contest in Modeling.

Teaching

Near Future:

Math 2930, Differential Equations for Engineers, Spring 2012.

Recent Past:

Math 4250 / CS 4210, Numerical Analysis and Differential Equations, Fall 2010.

Math 1220, Honors Calculus (2nd semester), Fall 2010.

Math 6140, Differential Games, Optimal Control, Front Propagation, & Dynamic Programming, Spring 2010.

Previously taught.

Research Interests

My work so far has been in Numerical Analysis, Non-linear PDEs, and Dynamical Systems.
A brief description of several recent projects can be found here.

What follows is an unsorted list of my other mathematical interests:

* Control Theory & Differential Games * Front Propagation Problems * Anisotropy & Homogenization * Bifurcation Theory * Dimension Reduction * Pareto & multi-modular optimization * Elimination Theory * Computability & Complexity * Approximate & Probabilistic Algorithms * Computational Geometry * Error Analysis

Publications

• J.A. Sethian and A. Vladimirsky.
  Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes. Proc. Natl. Acad. Sci. USA 97/11: 5699-5703 (2000).

• J.A. Sethian and A. Vladimirsky.
  Ordered upwind methods for static Hamilton-Jacobi equations. Proc. Natl. Acad. Sci. USA 98/20: 11069-11074 (2001).

• J.A. Sethian and A. Vladimirsky.
  Ordered Upwind Methods for Hybrid Control. 5th International Workshop, HSCC 2002, Stanford, CA, USA, March 25-27, 2002, Proceedings (LNCS 2289: 393-406).

• J.A. Sethian and A. Vladimirsky.
  Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory & Algorithms.
  SIAM J. on Numerical Analysis 41/1: 325-363 (2003).
  The first version had previously appeared as Center for Pure and Applied Mathematics Technical Report PAM-792 (University of California, Berkeley) in May 2001.

• J. Guckenheimer and A. Vladimirsky.
  A fast method for approximating invariant manifolds.
  SIAM J. on Applied Dynamical Systems 3/3: 232-260 (2004).

• B. Krauskopf , H.M. Osinga, E.J. Doedel, M.E. Henderson, J. Guckenheimer, A. Vladimirsky, M. Dellnitz, and O. Junge.
  A survey of methods for computing (un)stable manifolds of vector fields.
  Int. J. Bifurcation and Chaos 15(3): 763-791 (2005).

• A. Vladimirsky.
  Static PDEs for Time-Dependent Control Problems.
  Interfaces and Free Boundaries 8/3: 281-300 (2006).

• Z. Ren, S.B. Pope, A. Vladimirsky, and J.M. Guckenheimer.
  The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics. J. Chem. Phys. 124, 114111 (2006).
  (Small print: Copyright (2006) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.)

• Z. Ren, S.B. Pope, A. Vladimirsky, and J.M. Guckenheimer.
  Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport.
  Proceedings of the Combustion Institute 31, 473-481 (2007).

• A. Vladimirsky.
  Label-setting methods for Multimode Stochastic Shortest Path problems on graphs.
  Mathematics of Operations Research 33(4): 821-838 (2008).

• T. Sahai and A. Vladimirsky.
  Numerical methods for approximating invariant manifolds of delayed systems.
  SIAM J. on Applied Dynamical Systems 8/3: 1116-1135 (2009).

• A.M. Oberman, R. Takei, and A. Vladimirsky.
  Homogenization of metric Hamilton-Jacobi equations.
  Multiscale Modeling and Simulation 8/1: 269-295 (2009).

• A. Kumar and A. Vladimirsky.
  An efficient method for multiobjective optimal control and optimal control subject to integral constraints.
  Journal of Computational Mathematics 28/4: 517-551 (2010).

• A. Chacon and A. Vladimirsky.
  Fast two-scale methods for Eikonal equations.
  a shortened version accepted for publication by SIAM J. Sci. Comp.

• R. Takei, W. Chen, Z. Clawson, S. Kirov, and A. Vladimirsky.
  Optimal control with budget constraints and resets.
  submitted to SIAM J. on Control and Optimization.

An outdated programming resume (from my days as a software consultant).