People in the Department
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Office: 5514 French Hall
- PhD, University of Wisconsin at Madison, 1991.
Peer Reviewed Publications
- (Selected publications. If you have access to MathSciNet you can see other publications.)
- 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 of Computing Systems, Volume 57, Issue 2 (2015), 478 -- 520
- Computability aspects for 1st-order partial differential equations via characteristics (with S. Sun), Theoretical Computer Science, Volume 583, Issue C (2015), 27 -- 39
- On Computability of Navier-Stokes’ Equation (with S. Sun and M. Ziegler), Lecture Notes in Computer Science, Volume 9136 (2015), 334-342
- On Effective Convergence of Numerical Solutions for Differential Equations (with S. Sun), ACM Transaction on Computation Theory, Vol. 6, No. 1 (2014), 55 -- 80
- A Tribute to Marian Boykan Pour-El (1928 -- 2009) (with I. Pour-El), J. Logic Computation, first published online doi:10.1093/logcom/exs073 (2013)
- Computability and computational complexity of the evolution of nonlinear dynamical systems (with O. Bournez, D. S. Graca, and A. Pouly), Lecture Notes in Computer Science, volume 7921 (2013), 12 – 21
- Computability, Noncomputability, and Hyperbolic Systems (with D.S. Graca and J. Buescu), Applied Mathematics and Computation, 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), Theoretical 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 Proceedings in Mathematics, Vol. 1 (2011), 169 - 182
- Computability in planar dynamical systems (with D. S. Graca), Natural Computing, 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), Journal of Universal Computer Science, VOl. 15, Issue 6, 1301-1316, 2009.
- 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), Mathematical Logic Quarterly, 53(4-5), 511-531, 2007.
- Computable analysis of a boundary-value problem for the Korteweg-de Vries equation, Theory of Computing Systems, 41, 155-175, 2007.
- An algorithm for computing fundamental solutions (with K. Weihrauch), SIAM Journal on Computing, 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), Theoretical Computer Science, 332, 337-366, 2005.
- Computability theory of generalized functions (with K. Weihrauch), Journal of ACM, 50(4), 469-505, 2003.
- Is the wave propagator computable or can wave machines beat Turing machines (with K. Weihrauch)? Proceedings of the London Mathematical Society, 3(85), 312-332, 2002.
Experience & Service
- Member, Steering Committee for the international conference series Computability and Complexity in Analysis (http://cca-net.de) (01/01/2005 to Present) .
- Member of Editorial Board, Computability, the Journal of the Association Computability in Europe (http://www.computability.de/journal/) 08-2011 to Present