Recent research by our algebra group includes work on cryptography, quadratic forms, quantum groups, and Hopf algebras and their actions. The group's research has been funded by the National Science Foundation and the National Security Agency. The algebra group holds regular weekly research seminars.
- Jintai Ding: quantum groups, cryptography
- Tim Hodges: noncommutative algebra, quantum groups, cryptography
- Tara Smith: classical algebra, quadratic forms, Galois groups
The computational finance group is led by Professor Srdjan Stojanovic. His research interests lie in the area of "PDE methods in financial modeling"; more specifically: pricing, hedging, and portfolio optimization. The fundamental relationship between fair pricing and portfolio optimization is emphasized. A variety of financial instruments are studied: equity, bonds, foreign exchange, their derivatives, etc. To that end, a variety of mathematical areas are employed: nonlinear and linear differential equations (partial and ordinary), stochastic differential equations, stochastic control, computational methods (symbolic and numerical), etc.
- Srdjan Stojanovic: computational finance and nonlinear partial differential equations
- Yu-Juan Jien: stochastic processes and differential equations
- Joanna Mitro: probability and stochastic processes
- Ju-Yi Yen: probability; stochastic processes; mathematical finance
A wide variety of interdisciplinary research into mathematical and statistical aspects of the biosciences is conducted at UC. Our Mathematical Biology group studies mathematical modeling of complex physical phenomena. Don French studies numerical and computational models in neuroscience in collaboration with colleagues from the College of Medicine. Tony Leung studies problems in partial differential equations related to ecology and population dynamics. Sookkyung Lim uses scientific computation to study valveless pumping and flagellar movement. Steve Pelikan works in evolutionary genetics in collaboration with Steve Rogstadt from the Department of Biology.
Our statisticians work closely with colleagues researchers in medicine and environmental health on various aspects of biostatsitics. Jim Deddens' current interest is in developing statistical methodology in quantitative occupational epidemiology. For several years he has been collaborating with researchers at the National Institute for Occupational Safety and Health (NIOSH) on cancer mortality and ergonomic studies. Siva Sivaganesan works with colleagues at Children's Hospital and the Department of Environmental Health on applications of Bayesian Statistics. Paul Horn recently coauthored a book on the use of reference intervals in medicine.
- Mathematical Modeling
- Don French: computational neuroscience, finite element methods, finite difference methods
- Sookkyung Lim: scientific computation, valveless pumping, flagellar movement
- Stephan Pelikan: biomathematics, population genetics and structure
- Benjamin Vaughan: bacterial biofilms, biofluids, biomechanics, pattern formation, population modeling, modeling of biological method
- Yanyu Xiao: mathematical epidemiology and ecology; applied dynamical systems; agent-based modeling; machine learning