- 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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