Conferences and Seminars:

- Dynamical Systems Weekend
- Stability Criteria for Multi-Dimensional Waves and Patterns
- International Internet Seminar
- Emerging
Topics in Dynamical Systems and PDEs

**Book:**

- The Maslov index and the spectra of second order elliptic operators (with S. Sukhtaiev), Advances in Math. 329 (2018) 422-486 (PDF file)
- The Maslov index for Lagrangian paths in R^{2n} (with P. Howard and A. Sukhtayev) (PDF file)
- The Maslov and Morse indices for Schrodinger operator on R (with P. Howard and A. Sukhtayev) (PDF file)
- Hadamard-type formulas via the Maslov form (with A. Sukhtayev) (PDF file)
- Some results on the entropy of nonautonomous dynamical systems (with C. Kawan) (PDF file)
- The Morse and Maslov indices for Schroedinger operators with
matrix-valued potentials, J.
d’Analyse Mathem., 33 pp., to appear (with S. Sukhtaiev and A.
Sukhtayev) (PDF file)

- The Morse and Maslov indices for multidimensional Schroedinger
operators with matrix-valued potentials, Trans. Amer. Math. Soc., 60 pp., to
appear (with G. Cox, C. K. R. T. Jones and A. Sukhtayev)(PDF file)

- Operator bounds employing complex interpolation revisited, Operator Theory: Advances and Applications,
Collection of papers on the occasion of C. Batty 60-th birthday, W.
Arendt R. Chill and Y. Tomilov (editors), Birkhauser (to appear) (with
F. Gesztesy, F. Sukochev and Y. Tomilov) (PDF file)

- Stability of traveling waves in partly hyperbolic systems, Math. Model. Nat. Phenom. 8 (2013) 32 -- 48 (with A. Ghazaryan and S. Schecter) (PDF file)
- Finding eigenvalues of holomorphic Fredholm operator pencils
using boundary value problems and contour

integrals, Integral Eqns. Oper. Theory 78 (2014), 155 – 211 (with W.-J. Beyn and J. Rottmann-Matthes) (PDF file) - The Morse and Maslov indices for matrix Hill's equations, Proc. Symp. Pure Math., 87 (2013) 205 – 233 (with C. Jones and R. Marangell) (PDF file)
- Stability estimates for semigroups on Banach spaces, Discr. Cont. Dynam. Systems Ser. A, (J. Goldstein’s 70-th anniversary issue), 33, No. 11-12, (2013), 5203 – 5216 (with A. V. Yurov) (PDF file)
- The Evans function and the Weyl-Titchmarsh function, Discr. Cont. Dynam. Systems, 5 (2012) 939 - 970 (with A. Sukhtayev) (PDF file)
- The infinite dimensional Evans function, Journal of Functional Analysis 268 (2015) 1509–1586 (with A. Pogan) (PDF file)
- Derivatives of the Evans function and (modiﬁed) Fredholm determinants for ﬁrst order systems, Mathematische Nachrichten, 284 (2011) 1592 - 1638 (with M. Das) (PDF file)

- Functional models of non-selfadjoint operators, strongly continuous semigroups, and matrix Muckenhoupt weights, Izvestiya : Mathematics 75:2 (2011) 287–346 (with G. M. Gubreev) (PDF file)
- The index formula and the spectral shift function for relatively trace class perturbations, Advances in Mathematics 227 (2011) 319–420 (with F. Gesztezy, K. A. Makarov, F. Sukochev and Y. Tomilov) (PDF file)

- Stability of traveling waves for a class of reaction-diffusion systems that arise in chemical reaction models, SIAM J. Mathematical Analysis 42 (2010) 2434 - 2472 (with A. Ghazaryan and S. Schecter) (PDF file)
- Stability of traveling waves for degenerate systems of reaction diffusion equations, Indiana University Math. J., to appear (with A. Ghazaryan and S. Schecter) (PDF file)
- The algebraic multiplicity of eigenvalues and the Evans function revisited, Mat. Model. Nat. Phenom. 5 (2010) 269 - 292 (with A. Sukhtayev) (PDF file)
- Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics, Journal of Functional Analysis, 257 (2009) 3309–3328 (with R. Shvydkoy) (PDF file)
- Stability of gasless combustion fronts in one-dimensional solids, Archive Ration. Mech. Anal. 198 (2010) 981-1030. (with A. Ghazaryan, S. Schecter, and A. de Souza) (PDF file)

- Perturbations of strongly continuous operator semigroups, and matrix Muckenhoupt weights, Functional Analysis and Its Applications, 42 (2008) 234-238 (with G. Gubreev) (PDF file)

- Derivatives of (Modified) Fredholm Determinants and Stability of Standing and Traveling Waves, Journal de Mathematiques Pures et Appliquees, 90 (2008) 160-200 (with F. Gesztesy and K. Zumbrun)(PDF file)

- The spectral mapping property of delay semigroups, Complex Analysis Operator Theory, 2 (2008) 273–283 (with A. Batkai and T. Eisner)(PDF file)

- The Dichotomy Theorem for evolution bi-families, J. Differential Equations, 245 (2008) 2267-2306 (with A. Pogan)(PDF file)

- Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions, Discrete Continuous Dynamical Systems B, 9 (2008) 595 - 633 (with J. Pruss and R. Schnaubelt)(PDF file)

- Scattering in a forked-shaped waveguide, Integral Eqns. Operator Theory, 61 (2008) 365-399 (with V. Pivovarchik)(PDF file)

- Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions, J. Evolution Equations, 6 (2006) 535 - 576 (with J. Pruss and R. Schnaubelt)(PDF file)

- Dichotomy and Fredholm properties of evolution equations, J. Operator Theory, 58 (2007) 387 - 414 (with A. Pogan and R. Schnaubelt)(PDF file)

- Evans functions, Jost functions, and Fredholm determinants, Archive Ration. Mech. Anal., 182 (2007) 361 - 421 (with F. Gesztesy and K. A. Makarov) (PDF file)

- Non-self-adjoint operators, infinite determinants, and some
applications,

Russian J. Math. Phys. 12, No 4 (2005) 443-471 (with F. Gesztesy, M. Mitrea, and M. Zinchenko) (PDF file)

- Fredholm determinants and the Evans function for difference equations, Banach Center Publications, 75 (2007) 111-135 (with D. Cramer) (PDF file)

- Fredholm properties of evolution semigroups, Illinois J. Math., 48 (2004) 999-1020 (with Y. Tomilov) (PDF file)

- Regularization and frequency-domain
stability of well-posed systems, Math.
Control Signals Systems, 17
(2005) 128-151 (with
T. Randolph and R. Schnaubelt)
__(PDF file)__

- Fredholm differential operators with unbounded coefficients, J. Diff. Eqns., 208 (2005) 388-429 (with Y. Tomilov) (PDF file)

- Spectral analysis of Darboux transformations for the focusing NLS
hierarchy,
J
*. d'Anal. Math.*, 93 (2004) 139-197 (with F. Gesztesy, R. Cascaval, and H. Holden)__(PDF file)__

- The essential spectrum of the linearized 2D Euler operator is a
vertical
band.
*Contemp. Math.***327**(2003) 299-304__(PDF file)__

- Essential spectrum of the linearized 2D Euler equation and
Lyapunov-Oseledets
exponents,
*J. Math. Fluid.**Mech.*, 7 (2005) 164-178 (with R. Shvidkoy)**(PDF file)**

- Linear stability in an ideal
incompressible
fluid.
*Comm. Math. Phys.***233**(2003) 439--461**(PDF file)**

- Operator valued Fourier multipliers and
stability of strongly continuous semigroups, Integral Equations Operator Theory
51 (2005) 375-394
(with
F.
Raebiger)
**(PDF file)**

- A sharp formula for the essential
spectral
radius
of the Ruelle transfer operator on smooth and Holder spaces.
*Ergod. Theory and Dynam. Syst.***23**(2003) 175-191 (with V. M. Gundlach)**(PDF file)**

- Gearhart-Pruss Theorem in stability for wave equations: a survey.
In:
Evolution
Equations, G. Goldstein, R. Nagel, S. Romanelli (edts),
*Lect. Notes Pure Appl. Math.***234**(with D. Cramer)**(PDF file)**

- Hyperbolicity of semigroups and Fourier
multipliers,
In:
*Systems, Approximation, Singular Integral Operators,and Related Topics*, International Workhop on Operator Theory and Applications, IWOTA 2000, eds. Alexander A. Borichev and Nikolai K. Nikolski, Oper. Theory Adv. Appl.**129**(2001) 341--364 (with R. Shvydkoy).**(PDF file)**

- A spectral mapping theorem and invariant
manifolds
for nonlinear Schroedinger equations,
*Indiana Univ. Math. J.*, 49 (2000) 221--243. (with F. Gesztezy, C. Jones, and M. Stanislavova).**(PDF file)**