Project Title  Petascale experimental mathematics 
Summary  The growing field of applied algebra and algebraic geometry has created a large number of difficult computational problems. Applications in machine learning, quantum information, finance, and other areas demand computational solutions to algebraic problems that are several orders of magnitude larger than what is achievable on single machines. The intern will work on strategies for using petascale infrastructure to solve these problems. 
Job Description  The growing field of applied algebra and algebraic geometry has created a large number of difficult computational problems. Applications in machine learning, quantum information, finance, and other areas such as climate and computational biology demand computational solutions to algebraic problems that are several orders of magnitude larger than what is achievable on single machines. The intern will work on strategies for using petascale infrastructure to solve these problems. Algorithms include Groebner basis algorithms and adaptations of largescale sparse linear algebra to solve commutative algebra problems. The student will work with a professor, postdoc, and graduate student with complementary expertise on largescale computations for related families of polynomial systems arising particularly in quantum computing and machine learning/statistics. 
Conditions/Qualifications  Some abstract algebra coursework, experience with parallel programming of some kind. 
Start Date  05/15/2010 
End Date  05/15/2011 
Location  Penn State, State College, PA Website: http://www.math.psu.edu/morton/ 
Interns  Jacquelyn Kirchner
