The Department of Mathematics and Statistics has experts working on a variety of aspects of applied mathematics, including applied dynamical systems, mathematical biology and neuroscience, machine and statistical learning, mathematical physics, numerical analysis, partial differential equations, scientific computing, as well as stochastic processes and differential equations. Specific applications include long- and medium-scale asymptotics of fluid flows; models of neural dynamics, coding, and learning; particle-based immune and cellular signaling modeling; formation of coherent structures and patterns in fluids, chemical systems, morphogenesis, and neurological systems; random switching dynamics in bi-stable systems; asymptotics of learning in neural networks; and dynamics on quantum walks.

**Faculty:**

- Margaret Beck: dynamical systems including PDEs, stability, spatial dynamics, computer assisted proofs, and topological and geometric structures that govern solution behavior
- Ryan Goh: dynamical systems including applied PDEs, pattern formation and computation
- Sam Isaacson: numerical analysis, mathematical biology, and chemical physics, including particle-based stochastic reaction-diffusion models, jump process simulation methods, and modeling of immunological and cellular signaling networks.
- Tasso Kaper: dynamical systems including applied PDEs, multi-scale systems, pattern formation, delayed bifurcations, spatio-temporal canards, and multi-mode attractors
- Mark Kon: quantum probability and information, bioinformatics, machine and statistical learning, mathematical physics, mathematical and computational neuroscience, complexity theory, and wavelets
- Nancy Kopell: mathematical problems in neuroscience, including how does the brain produce its dynamics (physiological mechanisms), how do brain rhythms take part in cognition (sensory processing, attention, memory, motor control), and how can pathologies of brain dynamics help to understand symptoms of neurological diseases (Parkinson’s disease, schizophrenia, epilepsy) as well as alternate states of consciousness (anesthesia)
- Mark Kramer: mathematical and statistical neuroscience, including developing tools to understand the brain through analysis and modeling of neural data
- Michelle McCarthy
- Gabe Ocker: mathematical neuroscience, applied stochastic processes, and dynamics
- Ben Pittman-Polleta: temporal dynamics of brain activity, behavior, & cognition; computational models of neurophysiology & behavior, including biophysical models of neural circuits & rhythmic dynamics and probabilistic models of cognitive processes; brain rhythms and their interactions within and across frequencies; predictive processing, generative hierarchical modeling, & Bayesian inference in cognitive science & neuroscience; methods for measuring temporal dynamics in brain activity and behavior; speech processing, attention, goal-directed behavior
- Mickey Salins: probability theory, random processes, stochastic partial differential equations, large deviations
- Konstantinos Spiliopoulos: algorithmic and computational methods in machine and statistical learning, applied mathematics, stochastic processes and probability, financial mathematics, asymptotic problems for stochastic processes and (stochastic) partial differential equations such as multiscale methods and large deviations, statistical analysis, network modeling and statistical inference
- Gene Wayne: dynamical systems, partial differential equations, and mathematical physics

**Emeritus Faculty:**

- Stephen Grossberg: Brain models of learning; attention; cognition; emotion; consciousness; vision and image processing; audition, speech, and language; development; reinforcement learning; navigation; sensory-motor control and robotics; mental disorders (Alzheimer’s disease, autism, and schizophrenia). The models unify levels of brain organization from spikes and their synchronization to cognition. They are mathematically analyzed and transferred to applications in engineering, technology, and AI.

**Postdocs:**

- Montie Avery: dynamics of PDEs, pattern formation, and front propagation
- Caitlin Lienkaemper: mathematical neuroscience and geometry

**PhD Students:**

- Zachary Bezemek
- Cameron Edgar
- Alanna Haslam
- Max Heldman
- Ben Hosek
- Rob Jencks
- Vanny Khon
- Qianhan (Lanlan) Liu
- Hannah Pieper
- Eric Zhang