Utah2016_Projects

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title: Utah2016 Projects permalink: wiki/Utah2016_Projects/ layout: wiki

The following are topics that applicants have expressed an interest in working on at the workshop. This isn't a final list by any means, but we thought that this list might be helpful for applicants (especially people new to M2) to see what sort of things people want to work on:

• Noncommutative algebra (NCAlgebra, NCAlgebraV2), perhaps implementing some group rewriting algorithms (as in Herky, written in clisp) in M2 instead of calling bergman for those calculations.

• Algebraic combinatorics in general, and lattice polytopes. Relevant packages are "lattice polytopes", "Polymake", "hyperplane arrangements" . Special focus on computing Ehrhart polynomials and counting lattice points in polytopes.

• "Visualize" Create interactive visualizations of mathematical objects in modern browsers (i.e. graphs, posets). This project is almost complete.

• Linear Programing" This package will include methods such as the simplex method and integer programing.

• Work on "Complexes" package, the "SpectralSequences" package, and the "NormalToricVarieties package".

• Continuing the development of ""PosChar"" which implements various algorithms related to prime characteristic methods

Specifically, add methods that implement algorithms described in http://arxiv.org/abs/1509.01519 http://arxiv.org/abs/1307.6717 http://arxiv.org/abs/1301.1468 and more recent ongoing work on the calculation of global parameter test ideals.

• Improve Tensors package; initiate package for Noetherian operators and generalized inverse systems (as in http://arxiv.org/pdf/math/0411574.pdf).

• Constructing the section ring of a divisor

• "DGAlgebras" : adding functionality such as: H_n(A) as a H_0(A) module, (matric) Massey products, DG Algebra maps, and others.

• "LexIdeals": Speeding up the LexIdeal method, and adding an option for an upper degree limit irrespective of the default Gotzmann bound.

• "Splines": I am interested in the description of the work in this area at the last Macaulay conference.

• "GfanInterface"