RESEARCH ACTIVITIES

Jonathan Hauenstein

The current focus of Dr. Hauenstein's research is developing and implementing numerical and hybrid symbolic-numeric algorithms for computing and manipulating algebraic sets, and the application of these algorithms to solve large-scale problems arising in biology, engineering, and physics. Another focus of his research in the field of numerical algebraic geometry is to develop efficient methods for computing steady-state solutions to systems of partial differential equations.

More details: www4.ncsu.edu/~jdhauens

Loek Helminck

In the past 10 years most of Dr. Helminck's research has been an evolving study of symmetric spaces, their representations and applications. Symmetric spaces are also known as symmetric varieties or symmetric k-varieties when the base field k is not algebraically closed. These symmetric spaces play an important role in many areas of mathematics, including geometry, singularity theory and the cohomology of arithmetic subgroups. They are probably best known, however, for their role in representation theory.

- mathematical theories
- algorithms
- software libraries/packages

- Geometric study of differential and algebraic equations.
- Computational invariant theory: differential and algebraic invariants.
- Problems of equivalence and symmetry under group actions.
- Symmetry reduction of differential equations and variational problems.
- Geometric methods in computer image recognition and image processing.

Dr. Helminck's work is in symmetric varieties over algebraically closed fields includes geometric / invariant theoretical questions, as well as computational aspects. Much of his work is on symmetric k-varieties was motivated by studying p-adic symmetric k-varieties and their representations. Other fields of interest include infinite dimensional flag varieties, Caylely graphs and alternating forms.

More delails: www4.ncsu.edu/~loek/research/

Hoon Hong

Dr. Hong's current research goal is to develop

for efficiently solving non-linear constraints, arising in science and engineering, and declarative language design.

More details: www4.ncsu.edu/~hong/overview.html

Erich Kaltofen

Computational algebra and number theory; hybrid symbolic-numeric algorithms and code; sequential and parallel algorithms; symbolic manipulation systems and languages for research, industrial, and educational applications.

More delails: www4.ncsu.edu/~kaltofen/

Irina Kogan

Current Research Interests

More delails: www4.ncsu.edu/~iakogan/

- Differential and Difference Algebra

- Symbolic Computation

- Some other topics worked on

- Polynomial Vector Fields

- Sparse Interpolation

- Model Theory of Differential Fields

Michael Singer

Current Research Interests

More delails: www4.ncsu.edu/~singer/

Seth Sullivant

The main focus of Dr. Sullivant's research is on developing and applying techniques from algebra (in particular, algebraic geometry, commutative algebra, and combinatorics) to theoretical and computational problems in statistics and biology. Thus, his research falls under the scope of algebraic statistics and algebraic biology.

More delails: www4.ncsu.edu/~smsulli2/research.html

Agnes Szanto

The general objectives of Dr. Szanto's research program are to develop efficient algorithms for problems in algebra and in differential algebra, to analyze the computational complexity of the algorithms and to implement them.

Currently she is working on symbolic-numeric algorithms for the solution of certain polynomial and differential systems: these systems are given with limited accuracy and were traditionally called ill-conditioned. The goal is to find robust and efficient algorithms to solve them using the integration of numerical and symbolic techniques.

More delails: www4.ncsu.edu/~aszanto

Department of Mathematics

2108 SAS Hall

2311 Stinson Drive

Box 8205, NC State University

Raleigh, NC 27695-8205

**Phone** (919) 515-2382**
Fax **(919) 513-7336

student resources :

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courses

suggested curriculum

phd projects

application procedure

financial assistance

employment resources