An example of transformational acoustics, demonstrating near field bending of an incoming plane wave. Principal Investigator: Clyde Scandrett
Research - Applied Mathematics
Research Groups
The department's research efforts can be grouped into three broad areas, as delineated below. These areas have considerable overlap and several faculty consider themselves associated with more than one group. Beyond the areas listed below, a number of researchers from the department have major interdisciplinary connections to researchers from other departments across the campus. Indeed there are very prominent collaborations with the departments of Computer Science, Defense Analysis, Electrical and Computer Engineering, Mechanical and Aerospace Engineering, Meteorology, Oceanography, Operations Research, and Physics.
For more information, please contact the Applied Math Dept Associate Chair for Research: Distinguished Prof. Frank Giraldo
Applied Analysis
Applied analysis is concerned with the interface between fundamental mathematical structures which rely on continuity and their use in the physical and social sciences. This research group has diverse interests that include asymptotic analysis, control theory, mechanics (fluid and orbital), and game theory. There are significant overlaps with the research group in Scientific Computing, and the mathematical foundations of machine learning have recently emerged as a new focal area of research.
Faculty Members in the Applied Analysis Group:- Wei Kang - Professor and Research Board Alternate
- Art Krener - Research Professor
- Caesar Aguilar (now a professor at SUNY Geneseo)
- Thomas Hunt (now at Hurricane Electric)
- Qi Gong (now a professor at University of California, Santa Cruz)
View slides from the Computational Issues in Nonlinear Control conference.
Adaptive Mesh Refinement (AMR) tracking a tracer across the surface of the Earth. Principal Investigator: Frank Giraldo
Discrete Mathematics
Discrete mathematics, sometimes called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Discrete mathematics is extensively used in a variety of critical applications such as cryptography, coding theory, combinatorics, network analysis, and search algorithms for the internet.
Faculty Members in the Discrete Mathematics Group:- Ralucca Gera - Professor, Department Chair, and Program Manager for the Network Science Academic Certificate
- Thor Martinesen - Associate Professor (Permanent Military Professor), Associate Provost Academic Affairs, Academic Council Alternate, and PhD Committee Member
- Pante Stanica - Professor, Program Manager for Secured Communications Certificate, and Chair of PhD Committee
- Tron Omland (Norwegian National Security Agency)
A few examples of Generalized Petersen graphs of skip 2, whose spectrum is now known. Principal Investigators: Ralucca Gera & Pante Stanica
Scientific Computing
Scientific Computing is the study of theories, computational methods, numerical algorithms, and other tools required to practically solve mathematical models of problems from science and engineering in a robust, accurate, and efficient manner. The primary goal is the development of novel techniques and approaches to approximation and efficient computation that are at the heart of modern science. This research group is primarily focused on the numerical solution of partial and ordinary differential equations, numerical linear algebra, and approximation theory. There are significant overlaps with the research group in Applied Analysis.
Current projects being worked on by the group include earthquake modeling (funded by NSF), the construction of scalable numerical methods for climate modeling (funded by NSF), the development of new governing equations and numerical methods for space weather (funded by DARPA), and the development of sub grid-scale processes for better understanding extreme weather events such as tropical cyclones using super-parameterization and scientific machine learning methods (funded by ONR).
Faculty Members in the Scientific Computing Group:- Anthony Austin - Associate Professor and Faculty Council Rep
- Robert Bassett - Associate Professor and OR Faculty Council Rep
- Carlos Borges - Professor
- Frank Giraldo - Distinguished Professor, Program Manager for Scientific Computing Certificate, Associate Department Chair, and Associate Chair for Research
- Lucas Wilcox - Professor, Academic Council Rep, and PhD Committee Member
- Hong Zhou - Professor
- Kiran Jadhav (now at Tridiagonal Software)
- Daniel Abdi (now at ESRL/NOAA)
- Felipe Augusto de Braganca Alves (now at the University of Sao Paolo)
- Sergey Charnyi (now at Siemens)
- Shiva Gopalakrishnan (now a professor at IIT Mumbai)
- Thomas Gibson (now at AMD)
- Soonpil Kang (now at Lawrence Livermore National Lab)
- James Kelly (now at NRL DC)
- Michal Kopera (now at a professor at Boise St.)
- Simone Marras (now at professor at NJIT)
- Andreas Mueller (now at the European Center for Medium-Range Weather Forecasting)
- Sohail Reddy (now at Lawrence Livermore National Lab)
- Maciek Waruszewski (now at Sandia National Lab)
Research Collaboration
There is a high degree of collaboration within the department which can be seen in the graph below that shows links between all of our faculty who have published jointly.
