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.

Permanent faculty and their research interests

  • Jason Cantarella Professor. Geometric knot theory, particularly random knots.
  • Joe Fu Professor. Integral geometry.
  • David Gay  Professor. Smooth and symplectic topology of 4-manifolds and associated 3-dimensional issues. Also interested in mathematical illustration and outreach, heavily motivated by low-dimensional geometry and topology.
  • Saar Hersonsky Professor. Conformal geometry, geometric structures in low-dimensional topology, geometry of negatively curved spaces, image science.
  • Gordana Matic  Professor. 4- and 3-manifolds, contact topology, Heegaard Floer homology.
  • Jennifer Royal Lecturer. Differential geometry.
  • Michael Usher Professor. Symplectic and contact geometry and topology, Hamiltonian dynamics, Morse theory and persistence.

Postdocs

  • Eduardo Fernández Fuertes Limited Term Assistant Professor. Contact geometry and topology.
  • Yuan Gao Limited Term Assistant Professor. Fukaya categories and Liouville manifolds.

Weekly Seminar Schedule

 

Research Areas


Additive Combinatorics

Additive Combinatorics and Discrete Analysis Research Group at the Department of Mathematics at the University of Georgia.


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.


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, Dynamical Systems, Mathematical Biology, Mathematical Ecology, Mathematical Finance, Machine Learning, Numerical Solutions to PDEs, Signal, Image and Video Processing, Sparse Solutions of Linear System, Energy Minimization Problems and Mathematical Models for Collective Behavior. The Applied Math group members are currently investigating various topics including stability in population dynamics models, network analysis, microbial community analysis, compressive sensing, deep learning for data approximation, stochastic filtering, multivariate spline methods for various applications, numerical methods for kinetic equations, existence/uniqueness/stability of energy minimizers and long time behavior of models for collective behavior.


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


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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