- Algebraic Geometry
- Commutative Algebra
- Computational Algebra
- Combinatorics
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- Embeddings and syzygies of
projective schemes.
- Birational morphisms,
blowing up, Macaulayfication and arithmetic Macaulayfication of schemes.
- Blow-up algebras,
Rees algebras, associated graded rings.
- Cohen-Macaulayness, Hilbert functions, defining equations
and minimal free resolution.
- Asymptotic behavior
of algebraic invariants.
- Regularity and
multi-graded regularity.
- Monomial ideals,
hyper-graphs and edge ideals.
- Interactions between
commutative algebra and combinatorics.
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