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: +34 954 55 71 95 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
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