The group conducts research in modern biology problems by tapping on strengths in combinatorics, probability and statistics. Our current interests include detection of functional signals in biological sequences and protein networks, algorithms and models for inference of gene duplication history and reconstruction of phylogenetic networks, and discovery of the topological and dynamic principles of transcriptional regulatory networks.
This multidisciplinary research group emphasizes the synergy of mathematics, engineering and computer science in the areas of imaging science, computer vision, information theory and learning. Topics of interest include wavelet frame methods in imaging science, compressive sensing, data assimilation, low rank matrix completion and their applications, time-frequency and scale-space methods in signal processing, human and computer vision, and the interplay between information theory and statistical learning.
The group works in the interface of mathematics with finance and economics. Topics of interest include pricing of financial derivatives, portfolio selection, risk measure, fixed income products, credit risk, trading strategy, games with imperfect information or with many players or with location problems, random matching of economic agents, incentive compatibility problems in a large market with asymmetric information.
The group focuses on the design and analysis of efficient, accurate and robust numerical methods and their applications to applied sciences and engineering. Topics include numerical linear algebra, computational fluid dynamics, computational materials science, multi-phase/complex fluids, computational quantum and plasma physics, control theory, analysis of finite element and spectral methods, analysis and modeling of complex energy landscapes and barrier-crossing events, multi-scale/multi-physics methods, and emerging applications.
The group works mainly on the analysis, design and implementation of algorithms for continuous optimization, possibly with stochastic variables. Topics of interest include conic programming and its applications, interior point methods, nonsmooth Newton methods, augmented Lagrangian methods, iterative methods for large linear systems of equations, feasibility problems, first order methods, stochastic gradient descend and data analysis.