The core group of AM^{2} members have **research expertise** covering mathematical analysis, partial differential equations, numerical analysis, applied probability, dynamical systems, multiscale modeling, high performance scientific computation, and numerical optimization with applications data science, machine learning, data science, imaging science, biology, and climate modeling, to name a few.

Members are also directly involved in **applications,** among others in image processing, computer tomography, data science and artificial intelligence, models of visual cortex and brain inspired neural networks, biology, fluid dynamics, geosciences, finance.

Some of the principal **research directions** of applied mathematics pursued at AM^{2 }are: predictive modeling and data science, numerical analysis and scientific computing, including methods for deterministic and stochastic PDE, numerical inverse problems, image processing, geometrical design, stochastic modelling, probability theory, stochastic processes and equilibrium and nonequilibrium statistical mechanics; Nonlinear PDE, harmonic analysis, dynamical systems, ergodic theory and mathematical physics, mathematical biology and ecology.