Luis Narváez Macarro

21 Pages·2016·0.14 MB·English

Luis Narv´aez Macarro
Curriculum Vitae (April 2022)
Contact details
Departamento de A´lgebra & Instituto de Matem´aticas (IMUS)
Facultad de Matem´aticas
Universidad de Sevilla
Campus Reina Mercedes
C/ Tarfia s/n
41012, Sevilla, Spain
Phone: [phone]
Email: [email protected]
Web page: http://personal.us.es/narvaez/
Personal data
Born: July 11th, 1957
Citizenship: Spanish
Research interests
Algebraic Geometry, Singularity Theory, Rings of Differential Operators, (cid:68)-modules, Perverse
Sheaves, de Rham cohomology, Hasse–Schmidt Derivations
Education
Universidad de Sevilla, Seville, Spain Bachelor’s Degree, July 1979
Mathematics
Universit´e de Paris 7, Paris, France Ph.D., October 1984
Mathematics
Thesis advisor: Lˆe Du˜ng Tr´ang
Universidad de Sevilla Seville, Spain Ph.D., October 1984
Mathematics
Thesis advisor: Jos´e L. Vicente C´ordoba
Positions
Member September 1997 – July 1998
Institute for Advanced Study, Princeton, U.S.A..
Full Professor June 1993 – current
University of Seville, Spain.
Maˆıtre de Conf´erences invit´e October 1988 – February 1989
Universit´e de Grenoble, France.
Assistant Professor June 1986 – June 1993
University of Seville, Spain.
Profesor encargado de curso October 1984 – June 1986
University of Seville, Spain.
1
Pre-doctoral fellow October 1980 – September 1984
Universit´e de Paris 7, France.
Profesor ayudante October 1979 – September 1981
University of Seville, Spain.
Research profiles
• MathSciNet
• ORCID
• ResearcherID
• Scopus
• Scholar Google
List of publications
(56) (with Ch. Chiu) Higher derivations of modules and the Hasse-Schmidt module. Michigan
Math. J., to appear. (arXiv.org: 2007.14171)
(55) (withA.Castan˜oDom´ınguezandC.Sevenheck)Hodge ideals of free divisors. Sel. Math. New
Ser. 28, 57 (2022). (First Online: 18 April 2022) (arXiv.org: 1912.09786)
(54) (with M.P. Tirado Hern´andez) On the bracket of integrable derivations. Journal of Algebra
574 (2021), 70–91. (First Online: 28 January 2021) (arXiv.org: 1912.11635)
(53) Hasse–Schmidt modules versus integrable connections. Rev. Mat. Complut. 34 (1) (2021),
75–98. (First Online: 16 December 2019) (arXiv.org: 1903.08985)
(52) (with M. Gros and J. Sebag) Arc Scheme and Bernstein Operators. Arc Schemes and Sin-
gularities, 279–295. Edited by J. Nicaise, D. Bourqui and J. Sebag. World Scientific, 2020.
(First Online: March 2020)
(51) Hasse-Schmidt derivations versus classical derivations. A Panorama of Singularities (Confer-
ence to Celebrate Lˆe Du˜ng Tr´ang’s 70th Birthday, February 7–10, 2017, University of Seville,
IMUS,Spain). EditedbyF.J.Castro-Jim´enez,D.Massey,B.TeissierandM.Tosun. Contem-
porary Mathematics, vol. 742, Amer. Math. Soc., Providence, RI, 2020, pp. 157-179. (First
Online: January 2020) (arXiv.org: 1810.08075)
(50) Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations. J. Pure
Appl. Algebra 224 (1) (2020), 320–361. (First Online: 7 May 2019) (arXiv.org: 1807.10193)
(49) (with C. Sevenheck) Tautological systems and free divisors. Advances in Mathematics 352
(2019), 372–405. (First Online: 13 June 2019) (arXiv.org: 1805.02101)
(48) A mini-course on Hasse-Schmidt derivations. Arcs, differential algebraic geometry and singu-
larities, September 11th to 14th, 2018, Sevilla, Spain.
(47) On Hasse–Schmidt derivations: the action of substitution maps, pp. 219–262 in (46), 2018.
(First Online: 19 September 2018) (arXiv.org: 1802.09894)
(46) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Festschrift for
Antonio Campillo on the Occasion of his 65th Birthday, Edited by Gert-Martin Greuel, Luis
Narv´aez Macarro and Sebasti`a Xamb´o-Descamps. Springer, Cham, 2018, xvi+604 pp.
(45) EnrecuerdodeAlexanderGrothendieck: Pr´ologoparaunalecturadesuvidayobra. LaGaceta
de la RSME 20 (2) (2017), 297–324.
(44) Differential Structures in Commutative Algebra. Mini-course at the XXIII Brazilian Algebra
Meeting, July 27 - August 1, 2014, Maring´a, Brazil.
(43) A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors. Advances
in Mathematics 281 (2015), 1242–1273. (First Online: 19 June 2015) (arXiv.org: 1201.3594)
2
(42) On the modules of m-integrable derivations in non-zero characteristic. Advances in Mathe-
matics 229 (5) (2012), 2712–2740. (First Online: 7 February 2012) (arXiv.org: 1106.1391)
(41) Integrable logarithmic connections with respect to a cusp. CourseattheProgramme“Algebraic
versusAnalyticGeometry”,ErwinSchr¨odingerInstituteforMathematicalPhysics,November
19 - December 13, 2011, Vienna, Austria.
(40) (with Z. Mebkhout) Le th´eor`eme du symbol total d’un op´erateur diff´erentiel p-adique. Rev.
Mat. Iberoamericana 26 (3) (2010), 825–859. (First Online: 31 December 2010)
(39) D-modules in dimension 1. Algebraic approach to differential equations, 128–178. Edited by
LˆeDu˜ngTr´ang(ICTP,Trieste,Italy). WorldScientific,2010. ISBN:978-981-4273-23-7. (Free
access)
(38) Hasse–Schmidt derivations, divided powers and differential smoothness. Ann. Inst. Fourier
(Grenoble) 59 (7) (2009), 2979–3014. (arXiv.org: 0903.0246)
(37) (withF.J.Calder´onMoreno)Onthelogarithmiccomparisontheoremforintegrablelogarithmic
connections. Proc. London Math. Soc., 98 (3) (2009), 585–606. (First Online: 29 October
2008) (arXiv.org: math/0603003)
(36) Linearity conditions on the Jacobian ideal and logarithmic-meromorphic comparison for free
divisors. Singularities I, Algebraic and Analytic Aspects (International Conference in Honor
of the 60th Birthday of Lˆe Du˜ng Tr´ang, January 8-26, 2007, Cuernavaca, M´exico), 245–
269. Edited by J.P. Brasselet, J.L. Cisneros-Molina, D. Massey, J. Seade and B. Teissier.
Contemporary Mathematics, 474, AMS, 2008. (arXiv.org: 0804.2219)
(35) (with F. Gudiel-Rodr´ıguez) Explicit models for perverse sheaves, II. Algebras and Represen-
tation Theory, 11(2) (2008), 149–178. (First Online: 8 August 2007)
(34) (with F. J. Calder´on Moreno) Algebraic computation of some intersection D-modules. Lec-
ture Notes in Computer Science, 4151 (2006), 132–143. (Enlarged version at: arXiv.org:
math/0604287)
(33) (with F. J. Calder´on Moreno) A mixed associativity formula for tensor products over two
Lie-Rinehart algebras. Ann. Univ. Ferrara -Sez. VII- Sc. Mat. 51 (2005), 105–118.
(32) (with M. Fern´andez-Lebr´on) Coefficient fields and scalar extension in positive characteristic.
Journal of Algebra, 285 (2005), no. 2, 819–834. (First Online: 4 February 2005) (arXiv.org:
math/0411323)
(31) (with F. J. Calder´on Moreno) Dualit´e et comparaison sur les complexes de de Rham logarith-
miques par rapport aux diviseurs libres. Ann. Inst. Fourier (Grenoble) 55(1) (2005), 47–75.
(arXiv.org: math/0411045)
(30) La Geometr´ıa Algebraica: punto de encuentro de las Matem´aticas. Memorias de la Real
Academia Sevillana de Ciencias (1998-2001), vol. 6, 85–103, 2005.
(29) (with A. Rojas Le´on) Continuous division of linear differential operators and faithful flatness
of (cid:68)∞ over (cid:68) . S´eminaires et Congr`es 8 (2004), 129–148.
X X
(28) The Local Duality Theorem in D-module Theory. S´eminaires et Congr`es 8 (2004), 59–87.
(27) E´l´ements de la th´eorie des syst`emes diff´erentiels g´eom´etriques, Cours du C.I.M.P.A., E´cole
d’´et´e de S´eville (1996). Edited by Philippe Maisonobe and Luis Narv´aez Macarro. S´eminaires
et Congr`es 8 (2004), xx+430 pages.
(26) (with M. Fern´andez-Lebr´on) Hasse-Schmidt Derivations and Coefficient Fields in positive
characteristics. Journal of Algebra 265 (2003), no. 1, 200–210. (First Online: 14 May 2003)
(arXiv.org: math/0206261)
(25) (with F. Gudiel-Rodr´ıguez) Explicit models for perverse sheaves. Rev. Mat. Iberoamericana
19 (2003), no. 2, 425–454. (First Online: 31 August 2003) (arXiv.org: math/0207023)
(24) (with M. Fern´andez-Lebr´on) Conservation of the noetherianity by perfect transcendental field
extensions. Rev. Mat. Iberoamericana 19 (2003), no. 2, 355–366. (First Online: 31 August
2003) (arXiv.org: math/0103099)
3
(23) (with F. J. Calder´on Moreno, D. Mond and F. J. Castro Jim´enez) Logarithmic Cohomology
of the complement of a plane curve. Comment. Math. Helv. 77 (2002), no. 1, 24–38. (First
Online: 31 March 2002)
(22) (with F. J. Calder´on Moreno) Locally quasi-homogeneous free divisors are Koszul free. Tr.
Mat. Inst. Steklova 238 (2002), Monodromiya v Zadachakh Algebr. Geom. i Differ. Uravn.,
81–85; translation in Proc. Steklov Inst. Math. 238 (2002), 72–77.
(21) (with F. J. Calder´on Moreno) The module (cid:68)fs for locally quasi-homogeneous free divisors.
CompositioMath. 134(2002),59–74. (Publishedonline: 4December2007)(arXiv: math/0206262)
(20) LaTeor´ıaAlgebraicadelosSistemasDiferencialesLineales. ActasdelEncuentrodeMatem´aticos
Andaluces, Vol. 1, pp. 143–184, Universidad de Sevilla, 2001 (ISBN: 84-472-0289-5).
(19) (with H. Hauser) Continuous division of differential operators. Ann. Inst. Fourier (Grenoble)
51 (2001), no. 3, 769–778.
(18) (with M. Gros) Cohomologie ´evanescente p-adique: calculs locaux. Rendi Conti Sem. Mat.
Univ. Padova 104 (2000), 71–90.
(17) (with Z. Mebkhout) Le th´eor`eme de continuit´e de la division dans les anneaux d’op´erateurs
diff´erentiels. J. Reine Angew. Math. 503 (1998), 193–236.
(16) Division theorem over the Dwork-Monsky-Washnitzer completion of polynomial rings and
Weyl algebras. Rings, Hopf algebras, and Brauer groups (Antwerp/Brussels, 1996), 175–191,
LectureNotesinPureandAppl. Math.,197,Dekker,NewYork,1998. (ISBN:9780824701536)
(Personal copy)
(15) (with F. J. Castro-Jim´enez) Homogenising differential operators. Prepub. Fac. Matem´aticas,
Secci´onA´lgebra, Computaci´on, Geometr´ıayTopolog´ıa, Univ. Sevilla, no 36, June, 1997. (See
also arXiv.org: 1211.1867).
(14) (with F. J. Castro-Jim´enez and D. Mond) Cohomology of the complement of a free divisor.
Trans. Amer. Math. Soc. 348 (1996), no. 8, 3037–3049.
(13) Algebraic geometry and singularities. Papers from the Third International Conference on
Algebraic Geometry held in La R´abida, December 9-14, 1991. Edited by Antonio Campillo
L´opez and Luis Narv´aez Macarro. Progress in Mathematics, 134. Birkh¨auser Verlag, Basel,
1996. xxii+407 pp. (ISBN: 3-7643-5334-1)
(12) (withF.J.Castro-Jim´enezandD.Mond)Cohomologie du compl´ementaire d’un diviseur libre.
C. R. Acad. Sci. Paris S´er. I Math. 320 (1995), no. 1, 55–58.
(11) Cycles ´evanescents et faisceaux pervers. II. Cas des courbes planes r´eductibles. Singularities
(Lille, 1991), 285–323, London Math. Soc. Lecture Note Ser., 201, Cambridge Univ. Press,
Cambridge, 1994. (Preprint version)
(10) (with Z. Mebkhout) Le t´eor`eme de constructibilit´e de Kashiwara. E´l´ements de la th´eorie des
syst`emes diff´erentiels. Images directes et constructibilit´e (Nice, 1990), 47–98, Travaux en
Cours, 46, Hermann, Paris, 1993. (ISBN: 2-7056-6213-8) (Preprint version)
(9) (with Z. Mebkhout) Sur les coefficients de de Rham-Grothendieck des vari´et´es alg´ebriques.
p-adic analysis (Trento, 1989), 267–308, Lecture Notes in Math., 1454, Springer, Berlin, 1990.
(8) (with Z. Mebkhout) La th´eorie du polynˆome de Bernstein-Sato pour les alg`ebres de Tate et de
Dwork-Monsky-Washnitzer. Ann. Sci. E´cole Norm. Sup. (4) 24 (1991), no. 2, 227–256.
(7) A note on the behaviour under a ground field extension of quasicoefficient fields. J. London
Math. Soc. (2) 43 (1991), no. 1, 12–22. (Erratum)
(6) (withZ.Mebkhout)D´emonstrationg´eom´etriqueduth´eor`emedeconstructibilit´e. In“Leformal-
isme des six op´erations de Grothendieck pour les (cid:68) -modules coh´erents”, 251–257. Travaux
X
en Cours 35. Hermann, Paris, 1989. (ISBN: 2-7056-6049-6) (Preprint version)
(5) (with Z. Mebkhout) Stabilit´e de la cat´egorie Db((cid:68) ) par RΓ . In “Le formalisme des six
X h Y,alg
op´erations de Grothendieck pour les (cid:68) -modules coh´erents”, 98–107. Travaux en Cours 35.
X
Hermann, Paris, 1989. (ISBN: 2-7056-6049-6)
4
(4) (with Z. Mebkhout) Th´eor`eme de dualit´e locale: Cas des k-alg`ebres noeth´eriennes r´eguli`eres.
In “Le formalisme des six op´erations de Grothendieck pour les (cid:68) -modules”, 42–55. Travaux
X
en Cours 35. Hermann, Paris, 1989. (ISBN: 2-7056-6049-6)
(3) Syst`emesdiff´erentielslin´eairessurunesurfacedeRiemann. Introduction`alath´eoriealg´ebrique
des syst`emes diff´erentiels (Plans-sur-Bex, 1984), 50–96. E´dit´e par Lˆe Du˜ng Tr´ang. Travaux
en Cours 34, Hermann, Paris, 1988. (ISBN: 2-7056-6048-8)
(2) Cycles´evanescentsetfaisceauxpervers: casdescourbesplanesirr´eductibles. CompositioMath.
65 (1988), no. 3, 321–347.
(1) Un calcul de cycles ´evanescents par rapport aux courbes planes irr´eductibles. Applications aux
faisceaux pervers. C. R. Acad. Sci. Paris S´er. I Math. 301 (1985), no. 5, 197–200.
Grants
• Research grant PID2020-114613GB-I00 (Arithmetic Geometry, D-modules ans Singularities)
2021-2025, Government of Spain.
• ResearchgrantMTM2016-75027-P(ArithmeticGeometry,D-modulesandSingularities)2017-
2020, Government of Spain.
• Research grant P12-FQM-2696 (Singularities, Arithmetic Algebraic Geometry and Represen-
tationTheory: Differential,Cohomological,CombinatorialandComputationalStructuresand
Methods) 2014-2017, Andalusian Government.
• Research grant MTM2013-46231-P (Algebraic Geometry and Arithmetic Geometry: Differen-
tial Methods, Singularities, Cohomology and Elliptic Curves) 2014-2016, Government of
Spain.
• ResearchgrantMTM2010-19298(RingsofDifferentialOperators,SingularitiesandArithmetic
Algebraic Geometry) 2011-2013, Government of Spain.
• Research grant MTM2007-66929 (D-modules, Singularities and Arithmetic Algebraic Geome-
try) 2008-2010, Government of
Spain.
• Research grant MTM2004-07203-C02-1 (Singularities of varieties and of algebraic or analytic
differential systems. Applications and interactions with other fields) 2005-2007, Government
of Spain.
• Research grant BFM2001–3207 (D-modules and cohomology of varieties) 2002-2004,
Government of Spain.
• ResearchgrantPB97–0723(DifferentialMethodsandStructuresinAlgebra, AlgebraicGeom-
etry and Singularities) 1998-2001, Government of
Spain.
• Research grant PB94–1435 (Differential Structures in Algebraic Geometry and Singularities)
1995-1997, Government of Spain.
• Research grant CHRX-CT93-0091 (Enveloping Algebras, Quantum Groups and Representa-
tion Theory) 1993-97, European
Union.
• Research grant PB90–0883 (Homotopical Study of the Milnor Fibration of Plane Curves:
explicit formulae) 1992-1993, Government of Spain.
• Research Group of the Andalusian Research Program FQM-218 (Algebraic Geometry, Differ-
ential Systems and Singularities) 2002- current, Andalusian
Government.
Ph.D. Theses
• M. P. Tirado Hern´andez (Leaps of the chain of m-integrable derivations in the sense of Hasse-
Schmidt). May 2019.
5
• A.Castan˜oDom´ınguez(AlgebraicD-modulesandCohomologyofDworkFamilies)(Co-advisor:
A. Rojas Le´on, Univ. Sevilla). July 2014.
• B. Rodr´ıguez Gonz´alez (Simplicial Descent Categories) (Co-advisor: V. Navarro Aznar, Univ.
Barcelona). December 2007.
• M. Fern´andez Lebr´on (Hasse-Schmidt Derivations, coefficients fields and scalar extension in
positive characteristics). March, 2002.
• F. Gudiel Rodr´ıguez (Explicit Description of t-Structures over Stratifed Spaces). February
2001.
• F. J. Calder´on Moreno (Logarithmic Differential Operators with Respect to a Free Divisor).
July 1997.
Graduate students
• M. Camu´n˜ez Triguero (Degree Final Dissertation: Geometr´ıa Algebraica y aplicaciones a la
Combinatoria), July, 2021.
• J.A. Florido Valenzuela (Degree Final Dissertation: Sobre el Nullstellensatz de Hilbert), July,
2021.
• A. Rend´on Rodr´ıguez de Molina (Degree Final Dissertation: El polinomio de Bernstein-Sato
de une singularidad), July, 2020.
• A. del Valle Rodr´ıguez (Beca de colaboraci´on & Degree Final Dissertation:
Unavisi´onactualsobrelospuntossingularesdeunaecuaci´ondiferenciallinealenunavariable
compleja), July, 2020.
• J. Benabent Guerrero (Alumno interno), Academic Year 2019-2020.
• J. Navas Orozco (Degree Final Dissertation: Curvas El´ıpticas y el Teorema de Mordell), July,
2019.
• J. E. Vargas Mag´an (Degree Final Dissertation: Teor´ıa de Representaciones de Grupos Fini-
tos), July, 2018.
• G. Soisnard (Higher Education Internship Mobility, ENS, Rennes, France & Sevilla, Spain:
Elliptic curves: Mordell-Weil Theorem), June-July 2017.
• L.CurquejoOtero(Becadecolaboraci´on&MasterFinalDissertation: Classificationofformal
meromorphic connections in one variable), July, 2017.
• L. Curquejo Otero (Degree Final Dissertation: Teor´ıa de Haces), July, 2016.
• M. P. Tirado Hern´andez (IMUS Fellowship: Introduction to the Theory of R[F]-modules),
October-December 2014.
• M. P. Tirado Hern´andez (Beca de colaboraci´on & Master Final Dissertation: On the Cancel-
lation Problem), Academic Year 2013-2014.
• M. P. Tirado Hern´andez (Degree Final Dissertation: Involutivity of the Characteristic Ideal),
June, 2013.
• M. M´erida Angulo (IMUS Fellowship), July, 2011.
• J. M. Garc´ıa Garc´ıa (Master Final Dissertation: Divided Powers Algebras), December, 2010.
• E. Rodr´ıguez Gonz´alez (IMUS Fellowship), September, 2010.
• A. Castan˜o Dom´ınguez (Master Final Dissertation: Recent Methods in p-adic De Rham Co-
homology), December, 2009.
• A. Castan˜o Dom´ınguez (Beca de colaboraci´on: The zeta function of a complete nonsingular
curve), Academic Year 2007-2008.
• B. Rodr´ıguez Gonz´alez (Master Final Dissertation: Simplicial Objects, an study towards de-
scent categories), June 2005.
6
• A. Rojas Le´on (On the continuity of division over rings of differential operators), June 2001.
• B. Rodr´ıguez Gonz´alez (Beca de colaboraci´on), Academic Year 2002-2003.
• B. Medrano Garfia (Beca de colaboraci´on), Academic Year 2002-2003.
• M.J.SotoPrieto(MasterFinalDissertation(Tesina): DifferentialOperatorsofInfiniteOrder
and the Jacobian Conjecture), June, 1997.
• M. Fern´andez Lebr´on (Master Final Dissertation (Tesina): Differentiations and coefficient
fields: a generalization of a result of H. Matsumura), September, 1993.
• F. Gudiel Rodr´ıguez (Master Final Dissertation (Tesina): On a local version of the Riemann-
Hilbert problem in one variable), September, 1991.
Seminars and courses
• Rings of differential operators and Hasse-Schmidt derivations (1 & 2), Differential Operators
in Commutative Algebra Seminar – DOCAS, 2 & 9 July 2021. (Recording 1, Recording 2)
• ElpolinomiodeBernstein-Satodeunasingularidad,SeminariodelDepartamentodeMatem´aticas,
Universidad de Murcia, 22 de febrero de 2018. (Video)
• LosanillosdeoperadoresdiferencialescomoA´lgebrasenvolventesdelasderivacionesdeHasse-
Schmidt,SeminariodeA´lgebra,DepartamentodeMatem´aticas,UniversidaddeMurcia,22de
febrero de 2018.
• Derivaciones de Hasse-Schmidt, Curso de especializaci´on, FAMAF, Universidad de C´ordoba,
Argentina, 4 - 6 diciembre 2017.
• Derivaciones asociadas a una derivaci´on de Hasse-Schmidt, Encuentro de Singularidades, De-
partamento de Matem´aticas & ICMAT, Universidad Aut´onoma de Madrid, 23 de febrero de
2017.
• Hasse-Schmidt derivations and differential operators in any characteristic, Seminar on Alge-
braic Geometry, RIMS, Kyoto, 2017.
• The Bernstein-Sato polynomial of a singularity: a mathematical gem, Chemnitzer Mathema-
tisches Colloquium, Fakult¨at fu¨r Mathematik der TU Chemnitz, 2016.
• Derivaciones de Hasse-Schmidt y anillos de operadores diferenciales, Curso de doctorado, De-
partamento de Matem´aticas, Universidad Aut´onoma de Madrid, 30 de Mayo - 3 de Junio de
2016.
• A´lgebras diferencialmente admisibles sobre un cuerpo de caracter´ıstica positiva, Seminario de
A´lgebra y Combinatoria, Departamento de Matem´aticas, Universidad Aut´onoma de Madrid,
2015.
• Algunasconsecuenciasenteor´ıade(cid:68)-m´odulosdepropiedadesdelinealidaddelidealjacobiano,
Seminario de Geometr´ıa Algebraica, Universidad de Barcelona, November, 2014.
• Sym´etrie des racines du polynˆome de Bernstein-Sato et dualit´e de (cid:68)-modules, S´eminaire
d’Alg`ebre, Topologie et G´eom´etrie, Univ. Nice-Sophia Antipolis, December, 2012.
• (cid:68)-modules and Singularities, Doc-course IMUS on Singularities and Applications, Sevilla,
July, 2012.
• Local Analytic Geometry, Algebraic versus Algebraic Geometry, Erwin Schr¨odinger Institut,
Viena, November-December 2011.
• Basic operations in (cid:68)-module theory, School on D-modules and applications in Singularity
Theory, Sevilla-Madrid, Spain, June-July 2011.
• Elproblemadelaintegrabilidaddeladerivacionesencaracter´ısticadistintadecero,Seminario
de A´lgebra, Departamento de A´lgebra, Universidad de Sevilla, November, 2010.
• ElproblemadelaintegrabilidadHasse-Schmidtdelasderivaciones,PrimerEncuentrodeDifer-
enciales y Singularidades, Departamento de Matem´aticas, Universidad Aut´onoma de Madrid,
July, 2010.
7
• TheBernsteinpolynomial: agadgetbetweenAnalysisandAlgebra,Fakult¨atfu¨rMathematik,
Universit¨at Wien, October, 2009.
• Derivaciones de Hasse–Schmidt y potencias divididas, Seminario de A´lgebra de la U.A.M.,
Departamento de Matem´aticas, Universidad Aut´onoma de Madrid, May, 2009.
• El problema de integrabilidad de las derivaciones en el sentido de Hasse-Schmidt, Seminario
deGeometr´ıaAlgebraicaySingularidades,DepartamentodeA´lgebra,Geometr´ıayTopolog´ıa,
Universidad de Valladolid, November, 2008.
• Condiciones de linealidad para el ideal jacobiano de una hipersuperficie y teorema de com-
paraci´on logar´ıtmica, Seminario de Geometr´ıa Algebraica de la U.C.M., Departamento de
A´lgebra, Universidad Complutense de Madrid, June, 2006.
• Fundamentos de la teor´ıa de (cid:68)-m´odulos sobre variedades (I, II y III), Seminario del Departa-
mentodeMatem´aticas,DepartamentodeMatem´aticas,UniversidaddeSalamanca,May-June,
2005.
• Singul¨are Differentialgleichungen, Institut fu¨r Mathematik, Univ. Innsbruck, July, 2005.
• Potencias divididas, operadores diferenciales y derivaciones de Hasse-Schmidt, Seminario de
Geometr´ıa Algebraica y Singularidades, Departamento de A´lgebra, Geometr´ıa y Topolog´ıa,
Universidad de Valladolid, December, 2004.
• Minicurso sobre las operaciones geom´etricas de la Teor´ıa de D-m´odulos, Curso de especial-
izaci´on, F.M.A.F., Universidad Nacional de C´ordoba, Argentina, April, 2004.
• Dualit´e des connexions logarithmiques par rapport aux diviseurs libres, Conferencia en el
Seminario de G´eom´etrie Alg´ebrique, I.R.M.A.R., Universit´e de Rennes, I, Francia, May, 2004.
• Ejemplos de ideales de tipo lineal en teor´ıa de singularidades, Seminario de A´lgebra, Depar-
tamento de Matem´atica, Universidad de Murcia, April, 2003.
• Geometr´ıa Algebraica y Ecuaciones Lineales en Derivadas Parciales, Coloquio del Departa-
mento de Matem´aticas, Departamento de Matem´atica, Universidad de Murcia, April, 2003.
• Aspectos algebraicos de los sistemas lineales de ecuaciones en derivadas parciales, Coloquio
del Departamento de Matema´tica, Departamento de Matem´atica, Facultad de Ciencias de la
Universidad de Lisboa, January, 2003.
• Descripci´on de las categor´ıas de haces perversos en t´erminos de categor´ıas cl´asicas, Curso de
especializaci´on, F.M.A.F., Universidad Nacional de C´ordoba, Argentina, August, 2000.
• ElproblemadeRiemann-HilbertenelmarcodelaTeor´ıade(cid:68)-m´odulos,SeminariodeMatem´aticas,
Departamento de Matem´atica, Facultad de Ciencias Exactas y Naturales, Universidad de
Buenos Aires, Argentina, September, 2000.
• R´esolutions explicites pour les modules (cid:68)fs associ´es aux diviseurs libres et localement quasi-
homog`enes, S´eminaire d’Analyse Alg´ebrique, UFR de Math´ematiques, Univ. Paris VI, June,
2000.
• Topological structure on rings of infinite order differential operators, Analysis Seminar, Dep.
of Mathematics, Univ. of Pittsburgh, February, 1998.
• De Rham Cohomology and Infinite Order Differential Operators, Members Seminar, Institute
for Advanced Study, Princeton, November, 1997.
• Teor´ıa de (cid:68)-m´odulos (I y II), Curso de Especializaci´on, Univ. de La Laguna, Vicerrec-
torado de Investigaci´on, Deptos. de Matem´atica Fundamental y An´alisis Matem´atico, Fac.
de Matem´aticas, La Laguna, October, 1996.
• Introduction`alath´eoriedes(cid:68)-modules,ColloquiumdelInstitutfu¨rMathematik,Univ. Inns-
bruck, April, 1996.
• PhD course Anillos de operadores diferenciales de orden finito e infinito, Programa de Doc-
torado “Algebra y An´alisis”, Fac. Ciencias Experimentales, Almer´ıa, June, 1996.
• Surlastructuretopologiquede(cid:68)∞etapplications,S´eminairedeG´eom´etrieAlg´ebrique,U.F.R.
de Math. de l’Univ. de Nice (France), March, 1996.
8
• Interpretaci´on del complejo de De Rham logar´ıtmico respecto de un divisor libre, Seminario
de Geometr´ıa, Centro de Mat. e Aplica¸coes Fund., Univ. de Lisboa, December, 1995.
• PhD course Curvas Algebraicas, Programa de Doctorado “Matem´aticas”, Fac. Ciencias Ex-
perimentales, Univ. Almer´ıa, September, 1994.
• Quelques propri´et´es de finitude des op´erateurs diff´erentiels lin´eaires d’ordre infini (I, II), Sem-
inariodeGeometr´ıa,CentrodeMat. eAplica¸coesFundamentais,Univ. deLisboa,November-
December, 1993.
• Divisi´ondeoperadoresdiferencialesdeordeninfinitoyteoremadecomparaci´ondeGrothendieck-
Mebkhout,SeminariodeSingularidades-MesSingular,DepartamentodeAlgebrayGeometr´ıa,
Univ. Valladolid, June, 1993.
• Teoremas de finitud sobre los operadores diferenciales de orden infinito, Sem. de Algebra y
Teor´ıa de Nu´meros, Univ. Aut´onoma de Madrid, May, 1993.
• PhD course Curvas Algebraicas (Introducci´on a la Geometr´ıa Anal´ıtica local), Programa de
Doctorado “Matem´aticas”, Fac. Ciencias Experimentales, Almer´ıa, April & September, 1992.
• (cid:68)-m´odulos ycohomolog´ıa p-´adica, Sem. deGeometr´ıa Algebraica, Univ. deBarcelona, April,
1992.
• Teoremas de finitud en teor´ıa de (cid:68)-m´odulos, Sem. de Geometr´ıa Algebraica, Univ. Com-
plutense de Madrid, February, 1992.
• Cycles ´evanescents et Monodromie (I et II), S´eminaire de G´eom´etrie, U.F.R. de Math. de
l’Univ. de Nice (France), September-October, 1990.
• Cohomolog´ıadeDeRhamy(cid:68)-m´odulos,SeminariodelDepartamentodeAlgebrayGeometr´ıa,
Univ. Valladolid, June, 1990.
• Polynˆomes de Bernstein-Sato et corps de coefficients, Grupo de Trabajo de Algebra y Ge-
ometr´ıa, Instituto Fourier, Univ. de Grenoble I (France), April, 1990.
• LaTeor´ıadelPolinomiodeBernstein,SeminariodeAlgebra,ColegioUniversitariodeAlmer´ıa,
October, 1989.
• Uned´emonstrationg´eom´etriqueduth´eor`emedeconstructibilit´edeKashiwara(IetII),Groupe
de Travail d’Alg`ebre et G´eom´etr´ıe, Institut Fourier, Univ. de Grenoble I (France), December,
1988.
• Sobre el Teorema de constructibilidad, Seminario del Departamento de Algebra y Geometr´ıa,
Univ. Valladolid, June, 1987.
• Sobre el polinomio de Bernstein, Seminario del Departamento de Algebra y Geometr´ıa, Univ.
Valladolid, February, 1986.
• Exemples d’extensions de faisceaux pervers, S´eminare des Singularit´es de l’E´cole Polytech-
nique, Ecole Polytechnique, Palaiseau, Francia, June, 1984.
• Classification des germes de syst`emes diff´erentiels en dimension 1 (d’apr`es Brian¸con-Maiso-
nobe), S´eminare des Singularit´es de l’E´cole Polytechnique, E´cole Polytechnique, Palaiseau,
Francia, February, 1983.
Conference talks
• On Hasse-Schmidt derivations in nonzero characteristic, Singularities in Positive Character-
istic , CIRM, Luminy, 12-16 July, 2021. (Slides) (Recording)
• An attempt to make explicit the Riemann-Hilbert correspondence in rank 2 with singularities
along xp−yq =0, Rigid Local Systems, FCUL, Lisbon, 28 January-1 February 2019.
• A mini-course on Hasse-Schmidt derivations (I, II, III), Arcs, differential algebraic geometry
and singularities, IMUS, Sevilla, 11-14 September 2018.
• Rings of differential operators as enveloping algebras of Hasse-Schmidt derivations in arbi-
trary characteristics, Singularities, toric geometry and differential equations , TU Chemnitz,
Germany, 19-23 March 2018.
9
• SobrelaestructuraalgebraicadelasderivacionesdeHasse–Schmidt, Sesi´on“Geometr´ıaAlge-
braicayTeor´ıadeNu´meros”,PrimerEncuentroConjuntodelaRSMEylaUMA,Universidad
de Buenos Aires, Argentina, December 11-15, 2017.
• The Theory of Hasse–Schmidt Derivations, Encuentro Hispano–Cordob´es de Matem´atica ,
FAMAF, C´ordoba, Argentina, December 7-8, 2017.
• New insights on Hasse-Schmidt derivations, Colloquium 2017 Celebrating Contributions of
Antonio Campillo to Mathematics, IMUVA, Valladolid, Spain, June 23, 2017.
• Hasse-Schmidt derivations versus classical derivations, Special session “Algebraic Geometry
and Commutative Algebra”, Joint Meeting of Catalan, Spanish and Swedish Mathematical
Societies, Umea, Sweden, 12-15 June, 2017.
• Hasse–Schmidt derivations and differentials operators in any characteristic, A Panorama on
Singular Varieties: A conference to celebrate 70th Birthday of Lˆe Du˜ng Tr´ang, IMUS, Sevilla,
Spain, 7-10 February, 2017.
• Around the symmetry of the roots of Bernstein-Sato polynomials, D-modules and Hodge the-
ory, Kavli IPMU, University of Tokyo (Kashiwa campus), Japan, 23-27 January, 2017.
• Hasse-Schmidt derivations: an interesting notion to play with in non-zero characteristics, Arc
schemes and singularity theory, Rennes, France, 21-25 November, 2016.
• A look at rings of differential operators through Hasse-Schmidt derivations, Iberian Meeting
on Algebraic Analysis, Lisbon, Portugal, 8-10 June, 2016.
• On the right D-module structure on the top differential forms through Hasse–Schmidt deriva-
tions, D-modules and Singularities in honor of Michel Granger, Angers, Francia, 2-3 May,
2016.
• Una revisi´on de la memoria de Dedekind-Weber, Richard Dedekind (1831-1916) y el estruc-
turalismo en matem´aticas, IMUS, Sevilla, 27 abril, 2016.
• Differentiably admissible algebras over a field of positive characteristic, Special session “Dif-
ferential methods in Algebra and Algebraic Geometry”, First joint meeting SBM - SBMAC -
RSME, Fortaleza, Brazil, 7 - 10 December 2015.
• AdualityapproachtothesymmetryofBernstein-Satopolynomialsoffreedivisors, Multiplier
ideals, TestidealsandBernstein-Satopolynomials, UniversitatPolit`ecnicadeCatalunya, 7-10
September 2015.
• Differentiably admissible algebras in positive characteristic, D-modules in Commutative Alge-
bra, CIMAT, Guanajuato, M´exico, 10 - 14 August, 2015.
• Symmetries of the roots of b-functions: a survey, Differential and combinatorial aspects of
singularities, Technische Universit¨at Kaiserslautern, 3 - 7 August, 2015.
• Differential structures in commutative algebra, XXIII Escola de A´lgebra – Brazilian Algebra
Meeting, Universidade Estadual de Maring´a, Brasil, 27th July - 1st August, 2014.
• On the symmetry of the roots of Bernstein-Sato polynomials, Recent Trends in Algebraic
Analysis, Department of Mathematics, University of Padova, February 19-23, 2013.
• Symmetry properties of the roots of Bernstein-Sato polynomials and duality of D-modules,
Bruce 60 and Wall 75: An international workshop in Singularity Theory, its Applications and
Future Prospects, University of Liverpool, 18-22 June 2012.
• Symmetry of the roots of Bernstein-Sato polynomials and duality of D-modules, 6th Euro-
peanCongressinMathematics,Mini-symposiumon“DifferentialAlgebraandGaloisTheory”,
Krak´ow, July 2-7, 2012.
• Symmetry of the roots of b-functions associated with free divisors, Workshop on Free Divisors
and Differential Equations, Tokyo University of Agriculture and Technology, November 5-10,
2012.
• On the integrability of derivations in non-zero characteristics, Congreso del Centenario de la
RSME - Sesi´on especial de Singularidades, A´vila, 1-5 February, 2011.
10