Computer Algebra
Algorithmic methods in commutative algebra, including the study of resultant systems.
Research & software
Research
In ALCYON we work on Symbolic Computation, both on the mathematics that improves algorithms and on efficient, high-performance implementations that push mathematics further.
Symbolic Computation lies at the intersection of mathematics and computer science. This means that it is both 100% mathematics and 100% computer science.
Effective Algebraic Geometry
Singularities, real solving and the algorithmic tools needed to explore them, such as Hermite matrices and their signatures.
Optimization
Integer linear optimization. We use Polyhedral Omega to solve ILPs, and ILP to improve polynomial multiplication algorithms.
Polyhedral Geometry
Efficient computation with polyhedra, and polyhedral methods that improve algorithms across combinatorics and algorithm design.
Number Theory
Computational questions and algorithmic tools arising from integer partitions.
Software
We release our implementations as open source, from Polyhedral Omega and alcyon.jl to PTOPO and math-data.
How we work
Each project has theory goals, code deliverables and milestones. Members share updates every two weeks in the same format: progress, then blockers, then next steps. We hold ourselves to experiments others can reproduce, benchmarked results and a short technical report for every project.