- Commutative Algebra
- Computational Algebra
- Combinatorics
- Algebraic Geometry
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- Asymptotic behavior of algebraic invariant and properties.
- Regularity, asymptotic regularity of graded families of homogeneous ideals.
- Syzygies/free resolution, normality and Cohen-Macaulayness of embedded projective schemes.
- Ideal Containment Problem: symbolic and ordinary powers of ideals.
- Polynomial interpolations, Chudnovsky's and Demailly's Conjectures.
- Interactions between commutative algebra and combinatorics.
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