Mathematics Research at UGA

The faculty of the Mathematics Department are actively involved in creative research at the frontier of mathematical knowledge.  The department is loosely sectioned into the following research groups:

but a great deal of collaboration and communication crosses these boundaries.

Research Areas


Additive Combinatorics

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/


Algebra

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.


Algebraic Geometry

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.


Analysis


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.


Geometric Analysis

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.


Geometry

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.


Number Theory and Arithmetic Geometry

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 


Topology

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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