Paolo Lella
Associate Professor (professore associato)
Dipartimento di Matematica "F. Brioschi" Building 14 "La Nave", 4th floor Politecnico di Milano Piazza Leonardo da Vinci 32 IT-20133 Milano
+39 02 2399 4555 paolo [dot] lella [at] polimi [dot] it
News
Michele Graffeo, Sergej Monavari, Andrea Ricolfi, Alessio Sammartano and I are organizing the conference
The Geometry of the Hilbert Scheme of Points
in Levico Terme, May 6-10, 2024.
Experience
Associate professor (professore associato)
Mathematics Department, Politecnico di Milano
January 2021 - present
Tenured assistant professor (ricercatore RTD-B)
Mathematics Department, Politecnico di Milano
January 2018 - December 2020
Assistant professor (ricercatore RTD-A)
Mathematics Department, Università degli Studi di Torino
September 2017 - December 2017
INdAM postdoctoral fellow (assegnista di ricerca)
Mathematics Department, Università degli Studi di Torino
December 2016 - August 2017
Research collaborator (borsista di ricerca)
FIRB 2012 project "Differential Geometry and Geometric Function Theory"
August 2016 - November 2016
Postdoctoral fellow (assegnista di ricerca)
Mathematics Department, Università degli Studi di Trento
November 2014 - July 2016
Postdoctoral fellow (assegnista di ricerca)
Mathematics Department, Università degli Studi di Torino
March 2014 - October 2014
Postdoctoral fellow (assegnista di ricerca)
Mathematics Department, Università degli Studi di Torino
January 2013 - December 2013
Education
PhD in Mathematics
Università degli Studi di Torino
Thesis: Computable Hilbert schemes
2009 - 2012
Master Degree in Mathematics
Università degli Studi di Torino
2006 - 2008
Bachelor Degree in Mathematics
Università degli Studi di Torino
2003 - 2006
Publications
[IN PREPARATION] R. Ghiloni, P. Lella. Turning maps and approximation theory for slice functions.
[IN PREPARATION] M. Graffeo, P. Lella, S. Monavari, A.T. Ricolfi, A. Sammartano. Poset Hilbert schemes.
[IN PREPARATION] P. Lella. HilbertAndQuotSchemesOfPoints.m2 - A M2 package for Hilbert and Quot schemes of points in affine spaces.
[IN PREPARATION] C. Bertone, F. Cioffi, P. Lella. Computing marked families via sygyzy forecasting.
[PREPRINT] L. Giovenzana, F. Giovenzana, M. Graffeo, P. Lella. Unexpected but recurrent phenomena for Quot and Hilbert schemes of points, under review.
[PREPRINT] M. Graffeo, P. Lella, S. Monavari, A.T. Ricolfi, A. Sammartano. The geometry of double nested Hilbert schemes of points on curves, under review.
[ACCEPTED] L. Giovenzana, F. Giovenzana, M. Graffeo, P. Lella. A counterexample to the parity conjecture, Algebraic Geometry, 2024.
A. Boralevi, D. Faenzi, P. Lella. A construction of equivariant bundles on the space of symmetric forms, Rev. Mat. Iberoam., 3(38):761–782, 2022.
Y. Kambe, P. Lella. The Gröbner fan of the Hilbert scheme, Ann. Mat. Pura Appl., 200(2):547–594, 2021.
D. Alberelli, P. Lella. Strongly stable ideals and Hilbert polynomials, J. Softw. Algebra Geom., 9:1-9, 2019.
V. Beorchia, P. Lella, E. Schlesinger. The maximum genus problem for locally Cohen-Macaulay space curves, Milan J. Math., 86(2):137-155, 2018.
A. Boralevi, D. Faenzi, P. Lella. Truncated modules and linear presentations of vector bundles, Int. Math. Res. Not. IMRN, 17:5347-5377, 2018.
C. Fontanari, R. Ghiloni, P. Lella. A computational approach to the ample cone of moduli spaces of curves, Internat. J. Algebra Comput., 28(1):37-51, 2018.
P. Lella, M. Roggero. On the functoriality of marked families, J. Commut. Algebra, 8(3):367-410, 2016.
J. Brachat, P. Lella, B. Mourrain, M. Roggero. Extensors and the Hilbert scheme, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 16(1):65-96, 2016.
F. Cioffi, P. Lella, M.G. Marinari. A combinatorial description of finite O-sequences and aCM genera, J. Symbolic Comput., 73:104-119, 2016.
D. Agostini, D. Alberelli, F. Grande, P. Lella. The maximum likelihood degree of Fermat hypersurfaces, J. Algebr. Stat., 6(2):108-132, 2015.
F. Cioffi, P. Lella, M.G. Marinari, M. Roggero. Minimal Castelnuovo-Mumford regularity for a given Hilbert polynomial, Exp. Math., 24(4):424-437, 2015.
R. Hartshorne, P. Lella, E. Schlesinger. Smooth curves specialize to extremal curves, Math. Ann., 361(1-2):459-476, 2015.
P. Lella, E. Schlesinger. The Hilbert schemes of locally Cohen-Macaulay curves in $\scriptsize \mathbb{P}^3$ may after all be connected, Collect. Math., 64(3):363-372, 2013.
C. Bertone, P. Lella, M. Roggero. A Borel open cover of the Hilbert scheme, J. Symbolic Comput., 53:119-135, 2013.
C. Bertone, F. Cioffi, P. Lella, M. Roggero. Upgraded methods for the effective computation of marked schemes on a strongly stable ideal, J. Symbolic Comput., 50:263-290, 2013.
P. Lella. An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme, ISSAC 2012 - Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, 2012.
F. Cioffi, P. Lella, M.G. Marinari, M. Roggero. Segments and Hilbert schemes of points, Discrete Math., 311(20):2238-2252, 2011.
P. Lella, M. Roggero. Rational components of Hilbert schemes, Rend. Semin. Mat. Univ. Padova, 126:11-45, 2011.
Teaching
[2023-2024 spring] Algebra Lineare e Geometria (Linear Algebra and Geometry), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Mathematical Engineering.
[2023-2024 fall] Geometria (Geometry), Politechnic University of Milan, School of Civil, Environmental and Land Management Engineering, Bachelor of Science in Civil Engineering.
[2022-2023 spring] Algebra Lineare e Geometria (Linear Algebra and Geometry), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Mathematical Engineering.
[2022-2023 fall] Topologia Algebrica Computazionale (Computational algebraic topology), Politechnic University of Milan, School of Industrial and Information Engineering, Master of Science in Mathematical Engineering.
[2022-2023 fall] Geometria (Geometry), Politechnic University of Milan, School of Civil, Environmental and Land Management Engineering, Bachelor of Science in Civil Engineering.
[2021-2022 spring] Algebra Lineare e Geometria (Linear Algebra and Geometry), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Mathematical Engineering.
[2021-2022 spring] Analisi e Geometria 2 (Calculus and Geometry 2), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Aerospace Engineering/Energy Engineering/Mechanical Engineering.
[2021-2022 fall] Laboratorio di Geometria differenziale (Discrete Differential geometry), Politechnic University of Milan, School of Industrial and Information Engineering, Master of Science in Mathematical Engineering.
[2020-2021 spring] Analisi e Geometria 2 (Calculus and Geometry 2), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Aerospace Engineering/Energy Engineering/Mechanical Engineering.
[2020-2021 fall] Topologia Algebrica Computazionale (Computational algebraic topology), Politechnic University of Milan, School of Industrial and Information Engineering, Master of Science in Mathematical Engineering.
[2019-2020 spring] Algebra Lineare e Geometria (Linear Algebra and Geometry), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Mathematical Engineering.
[2019-2020 spring] Analisi e Geometria 2 (Calculus and Geometry 2), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Aerospace Engineering/Energy Engineering/Mechanical Engineering.
[2019-2020 fall] Laboratorio di Geometria differenziale (Discrete Differential geometry), Politechnic University of Milan, School of Industrial and Information Engineering, Master of Science in Mathematical Engineering.
[2018-2019 spring] Analisi e Geometria 2 (Calculus and Geometry 2), Politechnic University of Milan, School of Industrial and Information Engineering, Bachelor of Science in Aerospace Engineering/Energy Engineering/Mechanical Engineering.
[2018-2019 fall] Geometria (Geometry), Politechnic University of Milan, School of Civil, Environmental and Land Management Engineering, Bachelor of Science in Civil Engineering.
Complete list (also classes of previous academic years)