Actuarial, Investment, and Management Sciences
In this program, we examine the mathematics of decisions under
uncertainty in the actuarial, investment, and management sciences. We
explore the quantification and hedging of risk, the dynamic forces of
competition, and the pricing of derivative contracts that can be
traded to help individuals, businesses, financial institutions, and
speculators better manage their portfolios. This is a good area for
students with interests in stochastic processes, optimal control,
numerical analysis, and computation.
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Functional Data Analysis
Functional data analysis deals with statistical analysis in function
spaces. Projects in this group focus on interpolation, approximation,
estimation of functional data from a wide spectrum of applications and
seeks to develop statistical methods for multi-scale and multi-dimensional problems. This is a good area for students with interests
in data-rich fields such as medical imaging, geoscience, finance, and
sports.
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Mathematical Systems and Optimization
This group explores the mathematics of dynamical systems, control, and
optimization, as well as their application to a myriad of real-world
and scientiic problems. Of particular interest are mathematical,
statistical, and computational methods for approximation, learning,
prediction, and control. This is a good area for students with a
broad interests in applied mathematics, but also a taste for
mathematical rigor and abstraction.
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Nonlinear Waves and Coherent Structures
Nonlinear waves and coherent structures (or patterns) are ubiquitous
in nature and are studied in many fields, including: general
relativity, high-energy particle physics, fluid and solid dynamics,
plasma physics, nonlinear electrical circuits, Bose-Einstein
condensation, nonlinear and fiber optics, random media, ocean
dynamics, chemical reactions, population dynamics, and neuroscience.
In this program, we explore the existence and stability of nonlinear
waves and patterns, as well as the onset of instability as these
systems undergo changes, complex interactions, and/or disturbances.
This is a good area for students with interests in (nonlinear) partial
differential equations, dynamical systems, numerical analysis, and
computation.
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Computational Biology and Bioinformatics
Recent technological advances in the generation of biological data have revolutionized biomedical research at the cellular and molecular levels. The fields of computational biology and bioinformatics unify statistics and computer science in the analysis, integration, delivery and retrieval of biological information to describe or discover novel biological phenomena. Students in this group focus on the development and application of methods for the analysis of data from emerging genomic technologies and the application in biomedical research. Methodological interests include Bayesian methods, Hidden Markov models, dynamic programming algorithms, smoothing, mixture models, and high-performance computing. Applied interests are currently focused on topics in transcription regulation, epigenomics, developmental biology and cancer research. This is a good area for students interested in biology, biostatistics, bioinformatics, biomedical research or medicine.
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