Faculty members have contributed numerous articles to books and journals in theoretical and applied statistics, biophysics, chemistry, mathematics, geophysics, astronomy, genetics, neuroscience, bacteriology, biometry, public health, machine learning, artificial intelligence, imaging, psychology, sociology, medicine, law, history of science, education, and business. Rina Foygel Barber and Chao Gao work on problems in high dimensional statistical inference and their applications. Per Mykland uses his expertise in martingale theory and stochastic calculus to better understand financial markets. Yali Amit is developing fundamentally new approaches to computer vision and works on neural models for memory and recognition. Mary Sara McPeek studies genetic association and is a leader in understanding the statistical impact of family relations between sampled individuals. Matthew Stephens studies genetic association and population genetics and is a leader in the application of modern Bayesian methods in genetics, and in reproducible research and open science. Dan Nicolae studies genetic and environmental factors affecting human disease, and is co-chair of national and international asthma genetics consortiums. Wei-Biao Wu is developing novel mathematical approaches to the analysis of time series. Machine learning research is led by Rebecca Willett and Risi Kondor.
The department has expanded its horizons into various fields of computational and applied mathematics: John Reinitz is a mathematical biologist who studies mathematical models for the development of genetic expression patterns. Guillaume Bal and Lek-Heng Lim are applied mathematicians working on inverse problems theory and computational algebraic and differential geometry, respectively. Mary Silber studies dynamical systems with a focus on understanding mathematical mechanisms behind qualitative changes in system behavior, and Mihai Anitescu, who is joint with Argonne National Lab, studies nonconvex constrained optimization with application to large-scale problems in the energy domain.
Core Domains:
- Applied Dynamical Systems: Mary Silber
- Applied Probability: Guillaume Bal
- Partial Differential Equations: Guillaume Bal
- Probability: Steve Lalley, Greg Lawler
- Mathematical Statistics: Rina Foygel Barber, Peter McCullagh, Michael Stein, Stephen Stigler, Mei Wang, Wei‑Biao Wu
- Numerical ODE's and PDE's:
- Scientific Computation: Mihai Anitescu, Lek‑Heng Lim, Ronald Thisted
- Statistical Methodology: Rina Foygel Barber, Peter McCullagh, Mary Sara McPeek, Per Mykland, Dan Nicolae, Michael Stein, Matthew Stephens, Stephen Stigler, Wei‑Biao Wu
Interdisciplinary Domains:
- Biostatistics: Ronald Thisted
- Computational Chemistry:
- Computational Neuroscience: Yali Amit
- Environmental and Spatial Statistics: Mihai Anitescu, Mary Silber, Michael Stein, Mei Wang
- Inverse Problems and Imaging: Guillaume Bal
- Machine Learning and Pattern Recognition: Yali Amit, Rina Foygel Barber, Risi Kondor, Lek‑Heng Lim
- Mathematical Finance and Econometrics: Lars Hansen, Per Mykland, Wei‑Biao Wu
- Statistics and Genetics: Mary Sara McPeek, Dan Nicolae, John Reinitz, Matthew Stephens
