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Alessandro De Stefani

I am an Associate Professor and member of the Algebra & Geometry group in the Department of Mathematics at the University of Genova.

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Preprints & Publications

Preprints

  • Tight closure of products and F-rational singularities (w/ I. Smirnov). Submitted. arXiv: 2409.12787
  • Uniform bounds on projective dimension and Castelnuovo-Mumford regularity (w/ G. Caviglia). Submitted. arXiv: 2409.12787
  • From a local ring to its associated graded algebra (w/ M.E. Rossi & M. Varbaro). Submitted. arXiv: 2406.16421
  • Ladder determinantal varieties and their symbolic blowups (w/ J. Montaño, L. Núñez-Betancourt, L. Seccia & M. Varbaro). Submitted. arXiv: 2305.18167
  • On the rate of generic Gorenstein K-algebras (w/ M. Boij, E. De Negri & M.E. Rossi). Submitted. arXiv: 2304.14842
  • Jumping numbers of F-pure submodules (w/ D. Hernández, L. Núñez-Betancourt & E. Witt). Submitted.

Publications

  1. Bounds on the number of generators of prime ideals (w/ G. Caviglia).
    To appear in Amer. J. Math. arXiv: 2108.05683
  2. Blowup algebras of determinantal ideals in prime characteristic (w/ J. Montaño & L. Núñez-Betancourt).
    J. London Math. Soc. 110, no. 2 (2024). arXiv: 2109.00592
  3. A criterion for sequential Cohen-Macaulayness (w/ G. Caviglia).
    Archiv der Math. 123, no. 2 (2024), 137 - 145. arXiv: 2307.14483
  4. Purity of monoids and characteristic-free splittings in semigroup rings (w/ J. Montaño & L. Núñez-Betancourt).
    Math Z. 305, 31 (2023) arXiv: 2210.03358
  5. The Eisenbud-Green-Harris conjecture for fast-growing degree sequences (w/ G. Caviglia).
    Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol: XXV (2024), 1753 - 1762. arXiv: 2007.15467
  6. Frobenius methods in combinatorics (w/ J. Montaño & L. Núñez-Betancourt).
    São Paulo J. Math. Sci. 17 (2023), 387 - 429. arXiv: 2203.09902
  7. Stability and deformation of F-singularities (w/ I. Smirnov).
    Israel J. Math. (2024) arXiv: 2002.00242
  8. Global F-splitting ratio of modules (w/ T. Polstra & Y. Yao).
    J. Algebra 610 (2022), 773 - 792. arXiv: 1811.11022
  9. Global Frobenius Betti numbers and Frobenius Euler characteristics (w/ T. Polstra & Y. Yao)
    Michigan Math. J. 71(3) (2022), 533 - 552. arXiv: 1811.11022
  10. A uniform Chevalley theorem for direct summands of polynomial rings in mixed characteristic (w/ E. Grifo & J. Jeffries).
    Math. Z. 301 (2022), no. 4, 4141 - 4151. arXiv: 2104.00612
  11. On the notion of Sequentially Cohen-Macaulay modules (w/ G. Caviglia, E. Sbarra & F. Strazzanti).
    Res. Math. Sci. 9 (2022), no.3, Paper No. 40. arXiv: 2304.06609
  12. The Eisenbud-Green-Harris Conjecture (w/ G. Caviglia & E. Sbarra).
    Commutative Algebra 159 - 187, Springer Cham, (2021). arXiv: 2106.14759
  13. Linearly presented modules and bounds on the Castelnuovo-Mumford regularity of ideals (w/ G. Caviglia).
    Proc. Amer. Math. Soc. 150 (2022), 1397-1404. arXiv: 2104.13129
  14. A Cayley-Bacharach theorem for points in P^n (w/ G. Caviglia)
    Bull. London Math. Soc. 53 (2021), no. 4, 1185 - 1195. arXiv: 2006.14717
  15. F-stable secondary representations and deformation of F-injectivity (w/ L. Ma)
    Acta Math. Vietnam. 47 (2022), no. 1, 141 - 150 (special volume in honor of Nguyen Tu Cuong). arXiv: 2009.09038
  16. Decomposition of local cohomology tables of modules with large E-depth (w/ G. Caviglia)
    J. Pure Appl. Algebra 225 (2021), no. 6. arXiv: 2003.09626
  17. On monomial Golod ideals (w/ H. Dao)
    Acta Math. Vietnam. 47 (2022), no. 1, 359 - 367. arXiv: 1902.00806
  18. Decomposition of graded local cohomology tables (w/ I. Smirnov)
    Math. Z. 297 (2021), 1 - 24. arXiv: 1810.01536
  19. Cohomologically full rings (w/ H. Dao & L. Ma)
    Int. Math. Res. Not. IMRN 2021, no. 17, 13508 - 13545. arXiv: 1806.00536
  20. Local cohomology and Lyubeznik numbers of F-pure rings (w/ E. Grifo & L. Núñez-Betancourt)
    J. Algebra (special volume in honor of Craig Huneke) 571 (2021), 316 - 338. arXiv: 1710.00462
  21. A Zariski-Nagata theorem for smooth Z-algebras (w/ E. Grifo & J. Jeffries)
    J. Reine Angew. Math. 761 (2020), 123 - 140. arXiv: 1709.01049
  22. Globalizing F-invariants (w/ T. Polstra & Y. Yao)
    Adv. Math 350 (2019), 359 - 395. arXiv: 1608.08580
  23. F-signature function of quotient singularities (w/ A. Caminata)
    J. Algebra 523 (2019), 311 - 341. arXiv: 1804.01281
  24. On the existence of F-thresholds and related limits (w/ L. Núñez-Betancourt & F. Pérez)
    Trans. Amer. Math. Soc. 370 (2018), 6629 - 6650. arXiv: 1605.03264
  25. Symbolic powers of ideals (w/ H. Dao, E. Grifo, C. Huneke & L. Núñez-Betancourt)
    Springer Proc. in Math. and Stat. vol. 222 (2018), 387 - 432. arXiv: 1708.03010
  26. Generalizing Serre's splitting Theorem and Bass's cancellation theorem via free basic elements (w/ T. Polstra & Y. Yao)
    Proc. Amer. Math. Soc. 146 (2018), no. 4, 1417 - 1430. arXiv: 1608.08591
  27. F-thresholds of graded rings (w/ L. Núñez-Betancourt)
    Nagoya Math. J. 229 (2018), 141 - 168. arXiv: 1507.05459
  28. Frobenius Betti numbers and modules of finite projective dimension (w/ C. Huneke & L. Núñez-Betancourt)
    J. Commut. Algebra 9 (2017), no. 4, 455 - 490. arXiv:1412.4266
  29. A counterexample to a conjecture of Ding
    J. Algebra 452 (2016), 324 - 337. arXiv:1506.09168
  30. Products of ideals may not be Golod
    J. Pure Appl. Algebra 220 (2016), no. 6, 2289 - 2306. arXiv:1506.09129
  31. A sufficient condition for strong F-regularity (w/ L. Núñez-Betancourt)
    Proc. Amer. Math. Soc. 144 (2016), no. 1, 21 - 29. arXiv:1411.7078
  32. An algorithm for constructing certain differential operators in positive characteristic (w/ A.F. Boix & D. Vanzo)
    Matematiche (Catania) 70 (2015), no. 1, 239 - 271. arXiv:1503.01419
  33. Artinian level algebras of low socle degree
    Comm. Algebra 42 (2014), no. 2, 729 - 754. arXiv:1208.3506

Other

Curriculum Vitae

Employment

  • Since 1/2024: Università degli Studi di Genova - Associate Professor
  • 1/2021 - 12/2023: Università degli Studi di Genova - RTD B in Algebra
  • 3/2019 - 12/2020: Università degli Studi di Genova - RTD A in Algebra
  • 8/2018 - 2/2019: University of Nebraska, Lincoln (USA) - Postdoctoral Faculty Fellow
  • 8/2017 - 7/2018: University of Nebraska, Lincoln (USA) - Dale Jensen Postdoctoral Faculty Fellow
  • 8/2016 - 7/2017: Royal Institute of Technology, KTH (Sweden) - Postdoctoral Fellow

Education

  • 5/2016: University of Virginia (USA) - PhD in Mathematics. Advisor: Craig Huneke
  • 12/2012: University of Kansas (USA) - MA in Mathematics
  • 7/2010: Università degli Studi di Genova - Laurea Specialistica in Matematica. Advisor: M.E. Rossi
  • 7/2008: Università degli Studi di Genova - Laurea Triennale in Matematica. Advisor: M.E. Rossi

Grants and Awards

  • 1/2022 - 12/2024: Participant of PRIN 2020 project 2020355B8Y "Squarefree Gröbner degenerations, special varieties and related topics" (PI: Matteo Varbaro)
  • 1/2020 - 12/2021: FRA (Fondi di Ricerca di Ateneo) - Algebra Group
  • 8/2018-2/2019: AMS Simons Travel Grant
  • 10/2015: AMS Student Travel Grant
  • 9/2005 - 7/2008: Borsa INDAM for students enrolled in "Laurea Triennale in Matematica"

Visits and research meetings

Organization of scientific meetings

Lectures

  • 13-15/6/2022: 75+80=155 years of commutative algebra: a school and a conference dedicated to Winfried Bruns and Jürgen Herzog on the occasion of their 75th and 80th birthday. Three one-hour lectures on "Differential and symbolic powers of ideals"

Invited talks

  • 03/2024: Commutative Algebra Seminar - SLMath, Berkeley (USA). Link to video
  • 10/2023: Algebra Seminar - University of Hawai'i (online)
  • 5/2023: Workshop on Commutative Algebra and Algebraic Geometry in Prime Characteristics - ICTP, Trieste. Link to video
  • 2/2023: Resolutions in Local Algebra and Singularity Theory - MFO Oberwolfach (Germany)
  • 1/2023: Written Geometry: Commutative Algebra - CIRM Luminy, Marseille (France)
  • 5/2022: BIRS Workshop: Advances in Mixed Characteristic Commutative Algebra and Geometric Connections - Oaxaca (online). Link to video
  • 4/2022: Virtual Commutative Algebra seminars - IIT Bombay (online). Link to video
  • 4/2021: Commutative Algebra seminar - Purdue University (online)
  • 10/2020: Fellowship of the Ring - MSRI (online). Link to video
  • 8/2020: Virtual Commutative Algebra seminars - IIT Bombay (online). Link to video
  • 9/2019: Convegno UMI - Università di Pavia
  • 5/2019: Algebra seminar - Università degli Studi di Pisa
  • 2/2019: Commutative Algebra seminar - University of Nebraska, Lincoln (USA)
  • 12/2018: CMS Winter Meeting - Vancouver (Canada)
  • 11/2018: Commutative Algebra seminar - Purdue University (USA)
  • 7/2018: GTM Seminar - Politecnico di Milano
  • 5/2018: Giornate di Geometria Algebrica ed Argomenti Correlati XIV - Università degli Studi di Genova
  • 4/2018: AMS Sectional Meetings - Northeastern University (USA)
  • 4/2018: Commutative Algebra seminar - University of Nebraska, Lincoln (USA)
  • 3/2018: Mini-workshop - University of Virginia (USA)
  • 12/2017: Algebra seminar - Università degli Studi di Genova
  • 10/2017: KUMUNU 2017 - University of Kansas (USA)
  • 9/2017: Commutative Algebra seminar - University of Nebraska, Lincoln (USA)
  • 6/2017: Meeting of the Catalan, Spanish, Swedish Mathematical Society - Umeå University (Sweden)
  • 3/2017: Algebra and Geometry seminar - Royal Institute of Technology (Sweden)
  • 3/2017: AMS Sectional Meetings - College of Charleston (USA)
  • 3/2017: Algebra and Geometry seminar - CIMAT, Guanajuato (Mexico)
  • 12/2016: InterCity seminar - Université de Neuchâtel (Switzerland)
  • 10/2016: Commutative Algebra seminar - University of Utah (USA)
  • 10/2016: Commutative Algebra seminar - Purdue University (USA)
  • 10/2016: Commutative Algebra seminar - University of Michigan (USA)
  • 10/2016: Algebra seminar - University of Kansas (USA)
  • 7/2016: Algebra seminar - Università degli Studi di Genova
  • 4/2016: KUMUNUjr 2016 - University of Nebraska, Lincoln (USA)
  • 4/2016: Algebraic Geometry and Number Theory seminar - Clemson University (USA)
  • 3/2016: AMS Sectional Meetings - University of Georgia, Athens (USA)
  • 1/2016: AMS Joint Mathematics Meetings - Seattle (USA)
  • 12/2015: Algebra seminar - University of Kansas (USA)
  • 11/2015: Algebra seminar - Georgia State University (USA)
  • 11/2015: AMS Sectional Meetings - Rutgers University (USA)
  • 10/2015: Incontro di Algebra Commutativa - Università degli Studi di Genova
  • 10/2015: Commutative Algebra seminar - University of Utah (USA)
  • 10/2015: AMS Sectional Meetings - Loyola University, Chicago (USA)
  • 9/2015: Algebra seminar - University of Virginia (USA)
  • 7/2015: Algebra seminar - Università degli Studi di Genova
  • 4/2015: Commutative Algebra seminar - University of Michigan (USA)
  • 6/2013: Algebra seminar - Università degli Studi di Genova
  • 2/2013: Representation Theory, Homological Algebra, and Free Resolutions - MSRI, Berkeley (USA)
  • 11/2012: Workshop on Syzygies - Cornell University (USA)
  • 9/2012: KUMUNU 2012 - University of Missouri, Columbia (USA)
  • 4/2012: KUMUNUjr 2012 - University of Nebraska, Lincoln (USA)

A.A. 2024/2025

Primo semestre
Algebra 1
Algebra Commutativa 1

Previous years

Università degli Studi di Genova

  • Algebra Commutativa 2
  • Algebra Commutativa 1
  • Algebra 3
  • Geometria (Ingegneria Biomedica)
  • Algebra 1 (Esercizi)
  • Geometria (Ingegneria Informatica)
  • ALGA (Esercizi a Fisica)

University of Nebraska, Lincoln (USA)

  • Topics course on characteristic p>0 methods
  • Group theory
  • Intro to modern Algebra
  • Discrete mathematics for future HS teachers
  • Differential equations

Royal Institute of Technology - KTH, Stockholm (Sweden)

  • Minicourse on singularities and Frobenius

University of Virginia (USA)

  • Calculus I
  • Calculus II
  • Applied Calculus I

University of Kansas (USA)

  • KAP (Kansas Algebra Program)
  • Applied Calculus I