PhD, University of Wisconsin at Madison 1991
Theory of real computing; in particular, computability and complexity in
analysis and physics.
Peer Reviewed Publications
(Selected publications. If you have access to MathSciNet you can see other publications.)
Computing geometric Lorenz attractors with arbitrary precision ( with D. S. Graca and C. Rojas), Trans. Amer. Math. Soc. 370(2018), no. 4, 2955–2970
On sharpness of the local Kato-smoothing property for dispersive wave equations (with S.M. Sun, E. Trelat, and B.Y. Zhang), Proc. Amer. Math. Soc. 145(2017), 653 – 664
An analytic System with a Computable Hyperbolic Sink Whose Basin of Attraction is Non-Computable (with Daniel Graca), Theory Comput. Syst. Volume 57, Issue 2 (2015), 478 -- 520
Computability aspects for 1st-order partial differential equations via characteristics (with S. Sun), Theoret. Comput. Sci., Volume 583, Issue C (2015), 27 -- 39
On Computability of Navier-Stokes’ Equation (with S. Sun and M. Ziegler), Lecture Notes in Comput. Sci., Volume 9136 (2015), 334-342
On Effective Convergence of Numerical Solutions for Differential Equations (with S. Sun), ACM Trans. Comput. Theory, Vol. 6, No. 1 (2014), 55 -- 80
A Tribute to Marian Boykan Pour-El (1928 -- 2009) (with I. Pour-El), J. Logic Comput. 25(2015), no. 4, 1133 - 1140
Computability and computational complexity of the evolution of nonlinear dynamical systems (with O. Bournez, D. S. Graca, and A. Pouly), Lecture Notes in Comput. Sci.,, volume 7921 (2013), 12 – 21
Computability, Noncomputability, and Hyperbolic Systems (with D.S. Graca and J. Buescu), Appl. Math. Comput. 219 (2012), no. 6, 3039 –- 3054
The connection between computability of a nonlinear problem and its linearization: The Hartman-Grobman theorem revisited (with D.S.Graca and H.S.Dumas), Theoret. Comput. Sci. 457 (2012), 101 -- 110
Computability and Dynamical Systems (with J. Buescu and D.S. Graca), Dynamics, Games, and Science I, Mauricio Matos Peixoto, Alberto Adrego Pinto, David A. Rand (Eds.), Springer Proc. Math., Vol. 1 (2011), 169 - 182
Computability in planar dynamical systems (with D. S. Graca), Nat. Comput., Volume 10, Issue 4 (2011), 1295 -- 1312.
Computational unsolvability of domains of attraction of nonlinear systems, Proc. Amer. Math. Soc. 137 (2009), 2773-2783.
Topological complexity of blowup problems (with R. Rettinger & K. Weihrauch), J.UCS 15 (1009), no. 6, 1301-1316
Computability, noncomputability and undecidability of maximal intervals of IVPs (with D.S. Graca & J. Buescu), Trans. Amer. Math. Soc. 361(6), 2913-2927, 2009.
Computable analysis of the abstract Cauchy problem in Banach spaces and its applications I (with K. Weihrauch), MLQ Math. Log. Q. 53(4-5), 511-531, 2007.
Computable analysis of a boundary-value problem for the Korteweg-de Vries equation, Theory Comput. Syst., 41, 155-175, 2007.
An algorithm for computing fundamental solutions (with K. Weihrauch), SIAM J. Comput. 35(6), 1283-1294, 2006.
Computing Schrodinger propagators on type-2 Turing machines (with K. Weihrauch), J. Complexity 22(6), 918–935, 2006.
Computing the solution of the Korteweg-de Vries equation with arbitrary precision on Turing machines (with K. Weihrauch), Theoret. Comput. Sci., 332, 337-366, 2005.
Computability theory of generalized functions (with K. Weihrauch), J. ACM, 50(4), 469-505, 2003.
Is the wave propagator computable or can wave machines beat Turing machines (with K. Weihrauch)? Proc. London Math. Soc., 3(85), 312-332, 2002.
Member of Editorial Board, Computability, the Journal of the Association Computability in Europe (http://www.computability.de/journal/) Type:Editorial Service 08-2011 -To Present