Dr. Latushkin’ s mathematical interests are in applied analysis, and include operator theory, operator semi groups, control theory, infinite dimensional dynamical systems and differential equations, nonlinear partial differential equations, nonlinear waves, hydrodynamics, Lyapunov exponents, multiplicative Ergodic theorem, transfer operator. He authored over a hundred publications in pure and applied mathematics and graduated eight PhD students.
Dr. Latushkin has received several teaching awards including Purple Chalk-2007 (College of Arts and Science), Outstanding Teaching Award-2000 and -1995” (The Men of Engineering), and W. T. Kemper award for excellence in teaching (2000).
- 1982 Ph.D., Odessa University, Odessa, USSR., Mathematics
- 1978 M.S., Odessa University, Odessa, USSR, Mathematics and Education
- MATH 1500 Analytic Geometry and Calculus I
- MATH 1700 Calculus II
- MATH 2300 Calculus III
- MATH 4100 Differential Equations.
- Large variety of Graduate Level Courses
Dr. Latushkin’ s most recent research interests are concentrated on the spectral theory of differential operators that appear when one linearizes nonlinear partial differential equations about such special solutions as steady states and traveling waves and applications to spectral, linear and nonlinear stability of the solutions. This involves a combination of analytic and geometric methods such as the Evans function, spectral mapping theorems for strongly continuous operator semi groups, Maslov index, etc.
The index formula and the spectral shift function for relatively trace class pertur- bations, Advances in Mathematics 227 (2011) 319 – 420 (with F. Gesztezy, K. A. Makarov, F. Sukochev and Y. Tomilov).
Stability of gasless combustion fronts in one-dimensional solids, Archive Rational Mech. Anal. 198 (2010) 981 –1030 (with A. Ghazaryn, S. Shechter, and A. de Souza).
Derivatives of (modied) Fredholm determinants and stability of standing and trav- eling waves, J. Math. Pures Appl., 90 (2008) 160-200 (with F. Gesztesy and K. Zumbrun).
Evans functions, Jost functions, and Fredholm determinants, Archive Rational Mech. Anal., 182 (2007) 361-421(with F. Gesztesy and K. A. Makarov).
Evolution Semigroups in Dynamical Systems and Differential Equations, Math. Surv. Monogr. 70 AMS, Providence, RI, 361 pp., 1999 (with C. Chicone).