SCIENTIST IN CHARGE

WEB SITES OF THE GROUP

Gianfranco Casnati

Subgroup of Algebraic and Computational Geometry
Subgroup of Differential Geometry in Turin
Subgroup of Analysis, Mathematical Logic and Number Theory
Algebraic and Differential Geometry Seminars

TEAM

SHORT DESCRIPTION

Danilo Bazzanella
Riccardo Camerlo
Enrico Carlini
Simon Chiossi
Caterina Cumino
Antonio J. Di Scala
Massimo Ferrarotti
Letterio Gatto
Francesco Malaspina
Carla Massaza
Emilio Musso
Maria Luisa Spreafico
Giulio Tedeschi
Francesco Vaccarino
Paolo Valabrega

The research interests of the group concern algebraic, computational, differential and topological aspects of geometry. Topics of individual group members include: the study of algebraic varieties from both the intrinsic and embedded viewpoint; parameter spaces of low dimensional algebraic varieties (moduli spaces of curves and surfaces, Hilbert schemes of points and curves, Severi varieties); low codimensional projective subvarieties and vector bundles; intersection theory on Grassmannians and flag varieties; computational methods in commutative algebra and algebraic geometry; discrete differential geometry; Lie groups and algebras; Riemannian varieties with special holonomy; Kähler and symplectic geometry; descriptive dynamics and bifurcation theory; set theory and mathematical logic; topology of the real line and measure theory; analytic, algebraic and arithmetic methods in number theory (distribution of prime numbers, factorization methods for large numbers).

SOME RECENT PUBLICATIONS

E. Musso, L. Nicolodi: Hamiltonian flows on null curves. Nonlinearity 23(2010), no. 9, 2117–2129.
A.J. Di Scala, A. Loi: Kähler manifolds and their relatives. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010), no. 3, 495–501.
D. Bazzanella, A. Languasco, A. Zaccagnini: Prime numbers in logarithmic intervals. Trans. Amer. Math. Soc. 362 (2010), no. 5, 2667–2684.
E. Ballico, G. Casnati, R. Notari: Canonical curves with low apolarity. J. Algebra 332 (2011), 229–243.
C. Cumino, L. Gatto, A. Nigro: Jets of line bundles on curves and Wronskians. J. Pure Appl. Algebra 215 (2011), no. 6, 1528–1538.
E. Arrondo, F. Malaspina: Cohomological characterization of vector bundles on Grassmannians of lines. J. Algebra 323 (2010), no. 4, 1098–1106.
R. Camerlo: Dendrites as Polish structures. Proc. Amer. Math. Soc. 139 (2011), no. 6, 2217–2225.
E. Carlini, L. Chiantini, A.V. Geramita: Complete intersection points on general surfaces in P3. Michigan Math. J. 59 (2010), no. 2, 269–281.
M. Ferrarotti, E. Fortuna, L. Wilson: Algebraic approximation of germs of real analytic sets. Proc. Amer. Math. Soc. 138 (2010), no. 5, 1537–1548.
F. Galluzzi, F. Vaccarino: Hilbert-Chow morphism for non commutative Hilbert schemes and moduli spaces of linear representations. Algebr. Represent. Theory 13 (2010),no. 4, 491–509D.

RESEARCH PROJECTS

Coordination of international Research Projects

G. Casnati: Programma Vigoni 2005 "Metodi di algebra commutativa ed omologica in geometria", responsabile tedesco F. Catanese (Bayreuth).
A.J. Di Scala: "Sottovarieta' elicoidali dello spazio Euclideo" collaborazione scientifica Italia-Messico 2011-2013 (Ministero degli Affari Esteri)

Coordination of national Research Projects

F. Vaccarino: "XTERA-FOOD - Sviluppo tecnologie di food inspection", 2010-2013.
S. Salamon: PRIN 2007 "Geometria Differenziale e Analisi Globale".
S. Salamon: PRIN 2005 "Metriche Riemanniane e Varietà Differenziabili".

THESES

Ph.D. dissertations
D. Giovannini: Special structures and symplectic geometry. Advisor S. Salamon, 2004.
R. Di Nardo: Laudal type theorems for algebraic curves. Advisor P. Valabrega, 2004.
D. Conti: Special holonomy and hypersurfaces. Advisor S. Salamon, 2005.
T. Santiago: Schubert calculus on a Grassmann algebra. Advisor L. Gatto 2006
A. Gambioli: Grassmannians, Lie algebras and quaternionic geometry. Advisor S. Salamon, 2006.
F. Malapina: Monads and vector bundles on quadrics: cohomological splitting conditions. Advisors A.P. Rao e P. Valabrega, 2007.
L. Motto Ros: General reducibilities for sets of reals. Advisors A. Andreatta e R. Camerlo, 2007.
G. Mihaylov: Special Riemannian structures in six dimensions. Advisor S. Salamon, 2008.
T. Santiago: Schubert calculus on a Grassmann algebra. Advisor L. Gatto 2006.
F. Malapina: Monads and vector bundles on quadrics: cohomological splitting conditions. Advisors A.P. Rao e P. Valabrega, 2007.
L. Motto Ros: General reducibilities for sets of reals. Advisors A. Andreatta e R. Camerlo, 2007.
Suela Ruffa: Geometric Modeling and Partitioning of Mechanical Products. Advisor F. Vaccarino, 2009. Martina Gandini: Analysis of Process and Product Variability by Geometrical Hidden Features. Advisor F.Vaccarino, 2010.
Antonio Nigro: Sections of Grassmann Bundles. Advisor L. Gatto, 2010.

Master dissertations
P.C. Rossaro: Characterizaztion of critical points of the exponential map. Advisor S. Salamon, 2006.
A. Nigro: Luoghi di degenerazione nello spazio dei moduli delle curve. Advisor L. Gatto, 2006.
P. Crosetto: Cyclide and other surfaces modelled with Rhinoceros. Advisor S. Salamon, 2007.
A. Nigro: Luoghi di degenerazione nello spazio dei moduli delle curve. Advisor L. Gatto, 2006.
Alessia Gara: Riemannian frameworks for diffusion tensor imaging. Advisors L. Preziosi e F. Vaccarino, 2009.
Federica Marcolin: Face morphology analysis: soft-tissue landmark formalization. Advisors S. Moos, F. Vaccarino e E. Vezzetti, 2010.

Bachelor dissertations
L. De Mangos: Teoria di Galois. Advisor C. Massaza, 2004.
S. Ceolin: Numeri ordinali e loro aritmetica. Advisor R. Camerlo, 2005.
D. Manenti: I grafi e le loro colorazioni. Advisor R. Camerlo, 2005.
M. Scianna: La formula di Cauchy-Crofton e applicazioni. Advisor L. Gatto, 2006.
M. Radeschi: Algebra, analisi e geometria delle curve ellittiche. Advisor L. Gatto, 2006.
C. Repetti: Curve piane e funzioni speciali. Advisor S. Salamon, 2007.
L. Zanon: Assioma della scelta e insiemi non misurabili. Advisor R. Camerlo, 2008.
M. Scianna: La formula di Cauchy-Crofton e applicazioni. Advisor L. Gatto, 2006.
M. Radeschi: Algebra, analisi e geometria delle curve ellittiche. Advisor L. Gatto, 2006. L. Zanon: Assioma della scelta e insiemi non misurabili. Advisor R. Camerlo, 2008.
Yemeli Goula Léonce: Monografia sulla Crittografia: crittografia classica e crittografia moderna. Advisor L. Caire, 2008.
Mirko Antonino Biondo: Analisi e componenti indipendenti per lo studio delle firme tecnologiche. Advisor F. Vaccarino, 2010.
Roberta Sicuro: Analisi degli indicatori di processo per un centro di ricerca ICT. Advisor F. Vaccarino, 2010.
Eleonora Crevacore: An experimental study of plane Laguerre Geometry. Advisors E. Musso e F. Vaccarino, 2011.
Antonio Pace: Introduzione alla distribuzione dei numeri primi. Advisor D. Bazzanella, 2011.

SCIENTIFIC EVENTS

Meetings

New Perspectives on Holonomy and Submanifolds, Torino 2004.
Enumerative Geometry: Old and New, Torino 2004.
Logic Colloquium, Torino 2004.
AGaFe Meeting: Geometry of Algebraic Varieties, Ferrara 2005.
Syzygy 2005: Commutative Algebra and Algebraic Geometry, in honour of Paolo Valabrega, Torino 2005.
Set Theory and Analysis, Torino 2006.
Geometry Conference in honour of Nigel Hitchin, Madrid 2006.
Extremal Kähler Metrics and Kähler-Ricci Flow, Pisa 2008
Set Theory and Analysis, Torino 2006. G.T.M. Seminar: a Day on Commutative Algebra and Algebraic Geometry, Torino 2008.
Turin differential geometry day, Torino 2009.
G.T.M. Seminar: a Day on Commutative Algebra and Algebraic Geometry, Genova 2009.
Mathematica User Group Meeting, Padova 2009.
G.T.M. Seminar: Some Topics in Commutative Algebra and Algebraic Geometry, Torino 2010.
Mathematica User Group Meeting, Milano 2010.
Mathematica User Group Meeting, Torino 2011.
LEGAL (Liberdade em Geometria Algebrica), Rio de Janeiro 2011.

Workshops and Schools

Workshop on Zero-dimensional Schemes and Related Topics, Torino 2003.
School and Workshop on Polynomial Interpolation and Projective Embeddings, Torino 2003.
School and Workshop on Computational Methods in Algebraic geometry and Statistics, Torino 2004.
School and Workshop on Cremona Transformations, Torino 2005.
School and Workshop on Vector Bundles and Low Codimensional Varieties, Trento 2006.
School and Workshop on Geometry of Special Varieties, Trento 2007.
School and Workshop on Algebraic Stacks, Trento 2008.
GTM Seminar: a Day on Commutative Algebra and Algebraic Geometry, Torino 2008.
Mini-workshop on Riemannian metrics and differentiable manifolds, Torino, 2008.
School and Workshop on Vector Bundles and Low Codimensional Varieties, Trento 2006.
School and Workshop on Geometry of Special Varieties, Trento 2007.
School and Workshop on Algebraic Stacks, Trento 2008.
Mini-workshop on Riemannian metrics and differentiable manifolds, Torino, 2008.
School (and Workshop) on Hodge Theory and Algebraic Geometry, Trento 2009.
School (and Workshop) on Minimal Model Program and Shokurov's ACC Conjecture, Trento 2010.
ELGA 2011 (First Latin American School of Algebraic Geometry and its application). Buenos Aires/Cordoba 2011.
School (and Workshop) on Tropical and Toric Geometry, Trento 2011.

Future events

Riemann International School of Mathematics, Verbania, 2009.
INdAM Workshop on Kähler and Sasakian Geometry, Roma, 2009.
School and Workshop on Hodge Theory and Algebraic Geometry, 2009.
G.T.M. Seminar: Some Topics in Commutative Algebra and Algebraic Geometry, Torino 2012.
School (and Workshop) on Invariant Theory and Projective Geometry, Trento 2012.