Applied and Computational Mathematics (ACM)
The Department of Mathematics at USC offers a Ph.D. track in mathematics with concentration in applied and computational mathematics. This track was approved in the fall of 2009 as the result of an initiative to expand applied and computational mathematics into interdisciplinary areas. Students enrolled in the program can concentrate on either Applied Math, or Computational Math, or interdisciplinary mathematics during the course of their studies. The aims of this track are
The applied and computational mathematics faculty maintains a strong and vigorous research program in the following areas:
Many faculty members are engaged in interdisciplinary research activities and are affiliated with the Interdisciplinary Mathematics Institute and the NanoCenter at USC. The research of faculty and students is supported by the stateoftheart high performance computing and visualization facilities in the department, IMI and the NanoCenter. These include a high performance Linux cluster (256 processors) equipped with high powered Graphic Processing Units (Tesla cards), a visualization cluster (72 processors) of a tiled display wall, and a host of servers and workstations.
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ACM Faculty Members and Their Research Interests Peter Binev  Professor Ph.D., Sofia University, 1985 Research Interests: scientific computing, approximation theory, numerical analysis, nonlinear approximation, learning theory, high dimensional problems, numerical methods for PDEs, computer graphics, image, and surface processing. Colin Bennett  Distinguished Professor Emeritus Ph.D, University of Newcasle upon tyne, 1971 Research Interests: harmonic analysis, interpolation of operators, wavelets, history of mathematics. Eva Czabarka  Associate Professor Ph.D. University of South Carolina, 1998 Research Interests: extremal set theory, extremal graph theory, graph drawing, biological applications, statistical evaluation of retrieval algorithm. Wolfgang Dahmen  IMI Director of International Research Ph.D., RWTH Aachen, 1976 Research Interests: applied and numerical analysis, approximation theory, and interdisciplinary applications. Daniel Dix  Associate Professor Ph.D., University of Chicago, 1988 Research Interests: analysis, initial value problems for partial differential equations governing the evolution of nonlinear waves, asymptotic behavior of solutions, solutions with special symmetry, completely integrable equations, and solitons. Ronald DeVore  Robert L. Sumwalt Distinguished Professor Emeritus Ph.D., Ohio State University, 1967 Research Interests: approximation theory, applied harmonic analysis, image processing, and wavelets. Jerry Griggs  Carolina Distinguished Professor Ph.D., Massachusetts Institute of Technology, 1977 Research Interests: combinatorics, extremal set theory, extremal graph theory, graph coloring, and applications of discrete math to biology, number theory, analysis of algorithms, and communications. Xinfeng Liu  Associate Professor Ph.D., State University of New York at Stonybrook, 2006 Research Interests: scientific computing, high performance computing, interfacial phenomena, multiphase flows, computational biology, cellular dynamics. Lincoln (Linyuan) Lu  Professor Ph.D., University of California at San Diego, 2004 Research Interests: Random graph theory, computational combinatorics. Douglas Meade Associate Professor Ph.D., Carnegie Mellon University, 1989 Research Interests: applied mathematics, numerical methods for wave propagation on unbounded domains, nonoverlapping domain decomposition methods, and computer algebra systems. Lili Ju Professor Ph.D., Iowa State University, 2002 Research Interests: scientific computation and numerical analysis, exact boundary controllability problems for the wave equation, parallel algorithms and highperformance computing, and human brain imaging. Pencho Petrushev  Professor Ph.D., Sofia University, 1977 Research Interests: approximation theory, harmonic analysis, numerical methods with current focus on localized nonlinear approximation by waveletlike bases with applications to image processing, earth gravity models, and multiscale analysis of very large data. Robert Sharpley  Distinguished Professor Emeritus Ph.D., University of Texas at Austin, 1973 Research Interests: classical analysis, approximation theory, multiresolution analysis, signal and image processing, numerical analysis, visualization, and autonomous navigation. Yi Sun  Associate Professor László Székely  Professor Ph.D., Eötvös University, 1983 Research Interests: combinatorial geometry, graph drawing, phylogeny reconstruction, discrete probability, design and analysis of algorithms, combinatorial optimization, extremal problems (graphs and set systems). Paula Vasquez  Assistant Professor Ph.D., University of Deleware 2007 Research Interests: Applied and computational mathematics, Multiscale modeling and simulation of viscoelastic fluid flows, Viscoelastic and diffusive transport processes in pulmonary mucus and mucus simulants, Computational and mathematical biology
Hong Wang  Professor Ph.D., University of Wyoming, 1992 Research Interests: numerical analysis and differential equations, numerical approximation to differential/integral equations, and scientific computations. Qi Wang  Distinguished Professor Ph.D., Ohio State University, 1991 Research Interests: applied and computational mathematics, computational fluid dynamics and rheology of complex fluids, continuum mechanics and kinetic theories, multiscale modeling and computation of soft matter and complex fluids of anisotropic microstructures, biofluids and biomaterials, cell dynamics, parallel and high performance computing. Xiaofeng Yang  Associate Professor Ph.D., Purdue University, 2007 Research Interests: numerical analysis, high performance computing, multiphase flows, spectral methods for partial differential equations, phasefield methods. Zhu Wang  Assistant Professor Ph.D., Virginia Tech, 2012 Research Interests: Reduced Order Modeling, Climate Modeling, Numerical Analysis
