Paolo Mantero
Affiliation confirmed via AI analysis of OpenAlex, ORCID, and web sources.
Associate Professor
Also affiliated: University of California, Riverside (2013–2015); University of Notre Dame (2011); Shizuoka University (2017); University of Shizuoka (2017); Universidade Federal da Paraíba (2021); Smith College (2013); Purdue University West Lafayette (2011–2012); University of Virginia (2013–2014)
Research Areas
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Biography and Research Information
OverviewAI-generated summary
Paolo Mantero's research primarily investigates algebraic geometry, with a focus on commutative algebra and the properties of ideals and modules. His work explores concepts such as projective dimension, arithmetical rank, and the Cohen-Macaulay property, particularly in relation to structures presented by quadrics and hypergraphs.
Mantero has published on Chudnovsky's conjecture and the projective dimension of codimension two algebras. His research also delves into generalized stretched ideals and Sally's conjecture, as well as multiple structures with high projective dimension supported on linear subspaces. He has also investigated hypergraphs with high projective dimension and 1-dimensional hypergraphs.
Mantero has been a Principal Investigator and Co-Principal Investigator on two NSF grants totaling $61,600, supporting the Arkansas Spring Lecture Series in the Mathematical Sciences. He maintains an active lab website and has an h-index of 7 with 122 citations across 42 publications.
Metrics
- h-index: 8
- Publications: 40
- Citations: 155
Positions
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Associate Professor 2021–presentUniversity of Arkansas Department of Mathematical Sciences ORCID
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Assistant Professor 2015–presentUniversity of Arkansas Fayetteville Mathematical Sciences ORCID
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Visiting Assistant Professor 2013–2015University of California Riverside Mathematics ORCID
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Post-doctoral Member 2012–2013Mathematical Sciences Research Institute ORCID
Selected Publications
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A formula for symbolic powers (2024)
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The structure of Koszul algebras defined by four quadrics (2022)
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Betti numbers of the conormal module of licci rings (2021)
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The Alexander–Hirschowitz Theorem and Related Problems (2021)
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Betti numbers of Koszul algebras defined by four quadrics (2020)
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The structure and free resolutions of the symbolic powers of star configurations of hypersurfaces (2020)
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Singularities of Rees-like algebras (2020)
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The projective dimension of three cubics is at most 5 (2018)
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Hypergraphs with high projective dimension and 1-dimensional hypergraphs (2017)
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Arithmetical rank of strings and cycles (2017)
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A finite classification of (x, y)-primary ideals of low multiplicity (2017)
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Chudnovsky's conjecture for very general points in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msubsup></mml:math> (2017)
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A tight bound on the projective dimension of four quadrics (2017)
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Projective Dimension of String and Cycle Hypergraphs (2016)
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Generalized stretched ideals and Sally's conjecture (2015)
Federal Grants 2 $61,600 total
Conference: 50th Arkansas Spring Lecture Series in the Mathematical Sciences
Conference: 51st Arkansas Spring Lecture Series in the Mathematical Sciences
Collaboration Network
Top Collaborators
- A tight bound on the projective dimension of four quadrics
- A finite classification of (x, y)-primary ideals of low multiplicity
- The projective dimension of three cubics is at most 5
- Singularities of Rees-like algebras
- Projective Dimension of String and Cycle Hypergraphs
- Hypergraphs with high projective dimension and 1-dimensional hypergraphs
- Projective Dimension of String and Cycle Hypergraphs
- Chudnovsky's conjecture for very general points in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msubsup></mml:math>
- Generalized stretched ideals and Sally's conjecture
- Betti numbers of Koszul algebras defined by four quadrics
- The structure of Koszul algebras defined by four quadrics
- A tight bound on the projective dimension of four quadrics
- A tight bound on the projective dimension of four quadrics
- Chudnovsky's conjecture for very general points in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msubsup></mml:math>
- Singularities of Rees-like algebras
- Arithmetical rank of strings and cycles
- The Alexander–Hirschowitz Theorem and Related Problems
- Betti numbers of the conormal module of licci rings
- A formula for symbolic powers
- A formula for symbolic powers