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Tentative/possible
topics:
- Polytopes, fewnomials, toric varieties, sparse resultants.
- Polytopes
- Sparse resultants
- Binomial systems, intro to toric varieties
- Mixed volume
- Bernstein's theorem
- Fewnomials
- How to decompose a polynomial system?
- Primary decomposition
- Numeric irreducible decomposition
- Applications to...
- Economics: Nash equilibria
- Algebraic coding theory
- Integer programming
- Possible side topics:
- Proving identities in planar geometry via commutative
algebra.
- Counting multiplicities: can we do this numerically?
- Intro to tropical algebraic geometry
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