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Applied Mathematics

The Applied Mathematics Group in the Department of Mathematics at the University of Georgia has scientific interests in  Approximation Theory, Computational Math and High Performance Computing, Control Theory and PDE control, Data Analytics, Dynamical Systems,  Mathematical Biology, Mathematical Ecology,  Mathematical Finance, Machine Learning, Numerical Solutions to PDEs,  Signal, Image and Video Processing. The Applied Math group members are currently investigating various topics including  epidemiology and systems biology, stability in population dynamics models, systems ecology, network analysis, microbial community analysis, compressive sensing, deep learning for data analysis, video restoration, stochastic filtering, and multivariate spline methods for applications such as numerical solutions of partial differential equations, scattered data interpolation and fitting, image analysis, and curves and surfaces reconstruction.

Adams

Dr. Malcolm Adams

Professor

Research Interest:

  • Differential equations
  • Mathematical physics
  • Global analysis

  Email: mradams@uga.edu

 

Black

Dr. Kelly Black

Academic Professional

Research Interest:

  • Ecology
  • Modeling
  • Spectral Methods and PDE Approximation

  Email: kjblack@gmail.com

Hu

Dr. Weiwei Hu

Assistant Professor

Research Interest:

  • PDE control and Optimization
  • Optimal control
  • Computational methods
  • Flow control problems and network dynamics

  Email: weiwei.hu@uga.edu

Kazanci

Dr. Caner Kazanci

Associate Professor

Research Interest:

  • Biology and ecological modeling
  • Numerical analysis
  • Stochastic modeling

Email: caner@uga.edu

Lai

Dr. Ming-Jun Lai

Professor

Research Interest:

  • Multivariate splines and applications
  • Compressive Sensing
  • Numerical PDEs

  Email: mjlai@uga.edu

Mu

Dr. Lin Mu

Assistant Professor

Research Interest:

  • Computational fluid mechanics
  • Numerical PDEs
  • Computational biology

Email: linmu@uga.edu

Petukhov

Dr. Alexander Petukhov

Associate Professor

Research Interest:

  • Signal processing
  • Image/movie denoising
  • Machine learning

  Email: petukhov@math.uga.edu

Tie

Dr. Jingzhi Tie

Professor

Research Interest:

  • Analysis
  • Geometric analysis
  • Applied mathematics

  Email: jtie@math.uga.edu

Zhang

Dr. Qing Zhang

Professor

Research Interest:

  • Stochastic filtering and deep filtering
  • Applied probability
  • Mathematical finance

  Email: qz@uga.edu

Post Doctoral Associates and their fields of interest

Cuiyu He, Limited Term Assistant Professor, Ph.D. in Mathematics at Purdue University, 2017. Research Area: Adaptive mesh refinement and a Posteriori error estimation for finite element methods; Unfitted finite element methods including particularly CutFEM and IFEM; Shape optimization problem using unfitted FEMs; Local Flux Recovery for FEMs.

Bin Xie, Postdoctoral Research and Teaching Associate, Ph.D., Oklahoma State University, 2019.

Sofya Zaytseva, Limited Term Assistant Professor, Ph.D., Applied Science, College of William and Mary, 2019. 

current students

JINSIL LEE Ph.D. student working on compressive sensing

ZHAIMING SHEN Ph.D. student working on graph/network clustering.

KENNETH ALLEN Ph.D. student working on matrix completion

former ph.d. students

YIDONG XU Ph.D. Dec. 2019. working on optimization for multicariate splines for data fitting and numerical solution of PDE. His dissertation can be found HERE . Now he returns to China and is looking for an industry to work.

DANIEL MCKENZIE Ph.D. Aug. 2019 working on graph/network clustering. A PAPER BASED HIS DISSERTATION CAN BE FOUND HERE. IT IS PUBLISHED ON SIAM J. MATH. DATA SCIENCE IN 2020. Now he is a postdoc at UCLA. Check his webpage for more detail by clicking his name.

CLAYTON MERSMANN Ph.D. graduated in Aug, 2019 working on numerical solution of Helmholtz equation and Maxwell equations. SEE HIS DISSERTATION HERE. He is now an assistant professor atUniversity of South Florida.

ABRAHM VARGHESE Ph.D. in May, 2018 working on matrix completion. He graduated in May, 2018. His dissertation can be found HERE . He is now an assistant professor at Shenandoah University, Virginia.

JAMES LANTERMAN Ph.D. graduated in May, 2018 working on constructing smooth polygonal elements and polygonal splines over quadrilatral partitions. His dissertation can be found HERE . He works for IHG.

GEORGE SLAVOV Ph.D. graduated in Aug. 2016 working on numerical solution of diffusion-reaction equation and predator-prey system of PDE by using multivariate splines. HIS DISSERTATION TITLE IS "BIVARIATE SPLINE SOLUTION TO A CLASS OF REACTION-DIFFUSSION EQUATIONS." He is an instructor at Department of Mathematics, University of Georgia.

Phong Luu, Ph.D. in Mathematics, 2016, University of North Georgia.

LEOPOLD MATAMBA MESSI Ph.D. graduated in Aug. 2013 working on numerical solution of nonlinear PDE by using multivariate splines. He graduated in Aug. 2012. His dissertation title is "Theoretical and Numerical Approximation of the Rudin-Osher-Fetami model for image denoising in the continuous setting." He is a postdoc position at Mathematical Biology Institute, Ohio State University.

Duy Nguyen, Ph.D. in Mathematics, 2013, University of Massachusetts at Amherst.

QIANGYING HONG Ph.D., graduated in Aug. 2011. Her dissertation title is Bivariate Splines in variational models for image enhancements. She is now a lecturer at University of Kansas, Lawrenceville, Kansas.

LOUIS YANG LIU Ph.D., graduated in August, 2010. His dissertation is Non-convex Optimization for Linear System with Pre-Gaussian Matrices and Recovery from Multiple Measurements. He was an assistant professor at the College of William and Mary in fall, 2011 and Spring, 2012. He is now a visiting assisitant professor at Michigan State University.

Hoi Tin Kong, Ph.D. in Mathematics, 2010, AIG.
 

David Prager, Ph.D. in Mathematics, 2010, Anderson University.

BREE ETTINGER Ph.D., graduated in August, 2009. Her dissertation title is Bivariate Splines for Ozone Concentration Prediction. She is a postdoctorate at a university in Milan, Italy. She is now a lecturer at Department of Mathematics and Computer Science, Emory University.

Jie Yu, Ph.D. in Mathematics, 2009, Northern Trust Corporation.

DongHoon Shin, Ph.D. in Mathematics, 2009, Inha University, South Korea.

Lirong Yu, Ph.D. in Mathematics, 2009, Dalton State College.

Chao Zhuang, Ph.D. in Mathematics, 2008, BMO Financial Group.

HAIPENG LIU Ph.D., graduated in August, 2007. His dissertation title is Prewavelets for Numerical Solution of PDE's. He is a lecturer at Georgia State University.

JIANBAO WU Ph.D., graduated in August, 2007. His dissertation title is Spherical Splines for Hermite Interpolation and Surface Design.

OKKYUNG CHO Ph.D., graduated in August, 2006.Her dissertation title is Construction of Compactly Supported Multiwavelets.She is an assistant professor at Montgomery College.

JIE ZHOU Ph.D., graduated in August, 2006. His dissertation title is Construction of Orthonormal Wavelets of Dilation Factor 3 with Application in Image Compression and A New Construction of Multivariate Compactly Supported Tight Frame. He is a tenure track assistant professor at Coastal Carolina University in the fall, 2007.

VICTORIA BARAMIDZE Ph.D., graduated in August, 2005. Her dissertation title is Spherical Splines for Scattered Data Fitting. She is an associate professor at West Illinois University.

KYUNGLIN NAM Ph.D., graduated in August, 2005. Her dissertation title is "Tight Wavelet Frame Construction and Its Application for Image Processing". She was a visiting assistant professor at University of Toledo, Toledo, Ohio. Now she is an instructor at Baylor University.

Moustapha Pemy, Ph.D. in Mathematics, 2005, Towson University.

GERARD AWANOU Ph.D., graduated in August, 2003. His dissertation title is "Energy Methods for Numerical Solution of 3D Navier-Stokes Equations by Trivariate Splines". After post-doc working at IMA (Institute for Mathematics and its Applications) at the University of Minnesota for two years, he is now an associate professor at North Illinois University. He has been an associate professor at University of Illinois at Chicago since Fall, 2012.

Jianwu Wang, Ph.D. in Banking and Finance, 2003, J.P. Morgan.

XIANGMING XU Ph.D., graduated in May, 2001. His dissertation title is Construction of Two-Dimensional Non-separable of Orthonormal Wavelets of Short Support. He is a research scientist at Telchemy Inc., Sewanee, GA.

Ruihua Liu, Ph.D. in Mathematics, 2001, University of Dayton.

WENJIE HE Ph.D., graduated in August, 1998. His dissertation title is Compactly Supported Multivariate Multiwavelets: Theory and Constructions. He is now an associate professor at the Department of Mathematics and Computer Sciences, the University of Missouri at St. Louis, Missouri.

 

master degree students

RICHARD TATUM Masters of Applied Mathematics and Sciences, graduated in August, 1999. He now works at Naval Surface Warfare Center, VA.

VICTORIA BARAMIDZE Masters of Applied Mathematics and Sciences, graduated in August, 1999. Her thesis title is Existence, Uniqueness and Convergence of Cubic and Quintic Smoothing Splines . She is now a Ph.D., student of Dept. of Math., Univ. of Georgia.

KATHLEEN FARMER Masters of Sciences, graduated in August, 1997. Her thesis title is Scattered Data Interpolation by C2 Quintic Splines Using Energy Minimization. She is now an instructor at Department of Mathematics, North Lousiana State University.

JIANGXIANG LIU Masters of Sciences, graduated in August, 1995. He was a Ph.D., student at Dept. of Computer Sciences, Yale Univ. in Fall, 1995.

Research Areas

Additive Combinatorics and Discrete Analysis Research Group at the Department of Mathematics at the University of Georgia. Follow the following link for more information on this particular research area: https://research.franklin.uga.edu/additive-combinatorics/
The algebra group has a vibrant training program for graduate students and postdoctoral fellows. 
The algebra group has sponsored three NSF Postdoctoral Fellows: Wayne Wheeler (1996-98), David Hemmer (2001-03) and Jonathan Kujawa (2003-07). If you interested in applying to the Department of Mathematics at UGA for graduate studies or a postdoc, please do not hestitate to contact one of our faculty members.
Some focus areas of the Algebraic Geometry Research Group are moduli spaces, minimal model program, K3 surfaces and abelian varieties, combinatorial algebraic geometry. The group members also share a wide circle of interests with connections to arithmetic geometry, symplectic geometry and toplogy, combinatorics, and representation theory. For more information about this group, visit the following page http://research.franklin.uga.edu/agant/algebraic-geometry.
The Applied Mathematics Group in the Department of Mathematics at the University of Georgia has scientific interests in Approximation Theory, Computational Math and High Performance Computing, Control Theory and PDE control, Data Analytics, Dynamical Systems, Mathematical Biology, Mathematical Ecology, Mathematical Finance, Machine Learning, Numerical Solutions to PDEs, Signal, Image and Video Processing. The Applied Math group members are currently investigating various topics including epidemiology and systems biology, stability in population dynamics models, systems ecology, network analysis, microbial community analysis, compressive sensing, deep learning for data analysis, video restoration, stochastic filtering, and multivariate spline methods for applications such as numerical solutions of partial differential equations, scattered data interpolation and fitting, image analysis, and curves and surfaces reconstruction.
The Geometry Analysis group that is interested in: interactions between elliptic PDE's and differential geometry/topology, conformal geometry, minimal surfaces and other variational problems, CR geometry, geometric structures in low dimensional topology/dynamics, and geometric functional inequalities.
The interests of the Geometry research area group at the Department of Mathematics at the University of Georgia revolve around differential geometry, broadly construed. We have a weekly seminar that meets on Fridays at 2:30.
The Number Theory and Arithmetic Geometry group at the Department of Mathematics at the University of Georgia is interested in topics like the arithmetic of abelian varieties; torsion points, endomorphism algebras, Weil-Chatelet groups. Modular curves and Shimura curves. Period-index problems, and many others. Please click the following link for more information about this research area: https://research.franklin.uga.edu/agant/number-theory-and-arithmetic-geometry 
Each summer since 1961 we have hosted the Georgia Topology conference and every eighth year it's "the big one", a 2-week long festival of topology which we call the Georgia International Topology Conference.  For additional information see our conference webpage.

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