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.
- Ding, Jintai: quantum groups, cryptography
- Hodges, Tim: noncommutative algebra, quantum groups, cryptography
Quantitative & Mathematical Finance
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.
- Jien, Yu-Juan: stochastic processes and differential equations
- Mitro, Joanna: probability and stochastic processes
- Stojanovic, Srdjan: computational finance and nonlinear partial differential equations
- Yen, Ju-Yi: 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
- French, Don: computational neuroscience, finite element methods, finite difference methods
- Lim, Sookkyung: scientific computation, valveless pumping, flagellar movement
- Pelikan, Stephan: biomathematics, population genetics and structure
- Vaughan, Benjamin: bacterial biofilms, biofluids, biomechanics, pattern formation, population modeling, modeling of biological method
- Xiao, Yanyu: mathematical epidemiology and ecology; applied dynamical systems; agent-based modeling; machine learning