Foto del docente

Luca Migliorini

Full Professor

Department of Mathematics

Academic discipline: MAT/03 Geometry

Curriculum vitae

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CURRICULUM VITÆ

Luca Migliorini

Universita` di Bologna, Dipartimento di Matematica Piazza di Porta S.Donato 5, 40126 Bologna ITALY luca.migliorini@unibo.it

Place and date of birth : Firenze (Italy) June 3, 1961. Education:

  • Student in the Ph. D. Program in Mathematics, Universita` di Firenze, November 1987-May 1990; “Special student” under the direction of Y.T. Siu, January 1988– June 1989 at Harvard University, Cambridge (MA).

  • Laurea cum laude in Mathematics, 27 June 1985, Universit`a di Firenze. Compulsory Service in the Army April 1986-July 1987; Lieutenant since July 1986.

    Research interests

    Hodge theory, perverse sheaves and their applications to algebraic geometry and repre- sentation theory.

    Tenured Positions

    • 11/2001– : Universita` di Bologna: Full Professor.
    • 11/1999-10/2001 : Universita` di Trento: Associate Professor. • 05/1990–10/1999 : Universita` di Firenze: Research Fellow.

    Temporary positions and Invitations in the last ten years As a short time guest

    • 06/2013: Department of Mathematics, State University of New York at Stony Brook.

    • 02/2013 Institut fu ̈r Mathematik, University of Essen.

    • 02/2013 Institut fu ̈r Mathematik, University of Mainz.

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Affiliation:

Email: Telephone: Fax:

  • 05/2012 Max Planck Institut fu ̈r Mathematik, Bonn.

  • 04/ 2011: Mathematics Department, Instituto Superior T ́ecnico, Lisboa.

  • 03/ 2011: Mathematics Department, University of Gen`eve.

  • 01/2010, 02/2008: Mathematical Institute, Oxford University.

  • 04/2009: Institut des Mathematiques, Universit ́e de Gen`eve;

  • 11/2008: Mathematisches Institut, University of Bonn.

  • 02/2005: Institute for Advanced Study, Princeton.

    Invitations for longer periods

  • 02–04/2015 Member of the School of Mathematics of the Institute for Advanced Study, Princeton for the special year ”Topology of Algebraic varieties” organized by B. Totaro, C. Voisin.

  • 01–02/2014 Bernoulli Center of EPFL, Lausanne.

  • 09–10/2013, 01–02/2012 Max Planck Institut fu ̈r Mathematik, Bonn.

  • 02/ 2011, 09/2011: Mathematics Department, University of Freiburg.

  • 05/2010: Institut Henri Poincar ́e, Paris, for the ”Trimestre de G ́eom ́etrie Alg ́ebrique Complexe”.

  • 01–05/2007: Institute for Advanced Study, Princeton; Member of the School of Mathematics.

  • 12/2006: Centro Matematico E.De Giorgi, Pisa; Visiting Professor.

  • 10-11/2006, 9/2007: International Center for Theoretical Physics “Abdus Salam” in Trieste; Visitor.

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Invitations in the near future

• Plenary speaker at the conference of the Italian Mathematica Union, September 2015.

Scientific Activity
A selection of talks as invited speaker in international workshops in the last years

  • Workshop ”Refined invariants in geometry, topology and string theory”, BIRS, Banff (Canada), June 2013.

  • Workshop ”Recent trends in Algebraic Analysis” February 19-23, 2013, Padova

  • Workshop ”Geometria in Bicocca 2011” May 12-13 2011, Milano.

  • ”Journ ́ees Complexes Lorraines,” May 2-6 2011, Institut E ́lie Cartan, Nancy.

  • ”Workshop of Hodge theory”, ICTP (Trieste), July 2010.

  • “Workshop in complex geometry”, Korea Institute for Advanced Studies, Seoul, September 2009.

  • “Recenti progressi in geometria complessa differenziale e simplettica”, Pisa, Istituto E.de Giorgi February 2009.

  • “Topology of complex algebraic varieties”, Alghero, September 2006.

  • “Birational Geometry of Varieties”, Pisa, May 2006.

  • “Topology and differential geometry ”, Pisa Istituto E.de Giorgi, September 2004.

  • ”Algebraic cycles and motives” a conference in honour of J.Murre, annual EAGER workshop,

    Leiden August 2004.

  • ”Multiplier ideal sheaves in algebraic geometry and complex analysis” Oberwolfach April 2004.

Recent selected talks

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  • Talk at the Algebraic Geometry Seminar University of Brown, April 2015

  • Course at the Algebraic Geometry Seminar IAS Princeton February 2015.

  • Two talks at the Geometry seminar University of Mainz, February 2013,

  • Talk at the Geometry seminar University of Essen, February 2013,

  • Talk at the Geometry seminar Scuola Normale Superiore November 2012,

  • Talk at the Geometry seminar Universita` di Roma, Sapienza, November 2012,

  • Talk at the Geometry seminar E ́cole Polytechnique Federale Lausanne, September 2012,

  • Talk at the Geometry seminar Universita` di Pavia, May 2012,

  • Speaker at ”Seminario Fisico Matematico dell’Universita` di Milano”, March 2012,

  • Oberseminar Max Planck Institut fu ̈r Mathematik, Bonn, January 2012.

  • Talk in the Algebraic Geometry seminar of University of Zurich, September, 2011.

  • Geometry seminar at Istituto Superior Tecnico Lisbon, April, 2011.

  • two talks in the Geometry seminar Freiburg University, February 2011.

  • talk in the Algebraic Geometry seminar of the Max Planck Institut fu ̈r Mathematik in Bonn, November 2008.

  • talk in the Geometry seminar of the Mathematical Institute, University of Oxford, February 2008.

  • talk at “The Geometric Langlands Seminar,” University of Chicago, February 2007.

  • talk at ICTP “Abdus Salam,” Trieste, October 2006.

  • talk at “Institut Fourier,” Grenoble, May 2005.

  • talk at IAS Princeton, February 2005.

    Series of lectures in the last ten years

    • Five lectures on ”Hodge theory” for the School ”Derived Categories, Weyl Algebras and Hodge Theory” University of Warwick, UK

    • ”Hodge theory”, Course at the Scuola Normale Superiore di Pisa 4

  • Corso nella summer school ”Monodromy” del progetto ALGANT, a Dobbiaco, 23-27 Giugno 2014.

  • Corso nella Spring School ”Classical and p-adic Hodge theories”, presso il Centre H. Lebesgue dell’Universit ́e de Rennes, 19-23 Marzo 2014.

  • Mixed Hodge theory 5 lezioni, Bernoulli Center, EPFL Lausanne, Gennaio-febbraio 2014.

  • Perverse sheaves, nearby and vanishing cycles: 4 lectures at Universita` di Padova, April 2012.

  • Mixed Hodge theory and nonabelian Hodge theory of curves, three talks in the series ”Fables g ́eometriques”, Universit ́e de G ́en`eve, March 2011.

  • Hitchin fibrations, endoscopy and mirror simmetry, 4 lectures at the Mathematics Department, University of Roma ”Sapienza”, December 2010.

  • Course ”Hodge theory of maps”, joint with M.A. de Cataldo, at the ICTP (Trieste) Summer school in Hodge Theory, June 2010.

  • Unique lecturer of the winter school “The topology of algebraic maps, Perverse sheaves and the decomposition theorem”, University of Freiburg, 22-29 February 2010.

  • Minicourse on Hodge Theory: 2 lectures at Universit`e de Gen`eve, April 2009.

  • Topics on Mixed Hodge Theory: 4 lectures at Universita` di Padova, June 2007.

  • An introduction to Mixed Hodge Theory: 4 lectures at the ICTP “Abdus Salam” Trieste, October 2006.

  • Perverse sheaves and Hodge theory: 4 lectures at Universita` di Roma ”La Sapienza”, October-December 2003.

    Teaching Activity

  • Except for the sabbatical leaves n the spring term 2014-2015 and in the year 2006/2007 I have usually given two courses each year, one for the first level de- gree (“Laurea triennale”) in Mathematics, one for the second level degree (“Laurea specialistica”) in Mathematics.

  • I have been a member of the “Collegio Superiore” of the University of Bologna, a special program addressed to selected students, from 2002 to 2006and again from 2009 to present. In particular during these four years I have been tutoring a group of mathematics students (first and second level), for whom I organized special programs of lectures, reading courses and selected exercises sessions.

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• I supervised the graduation theses, for the first or second level degree in mathe- matics (both levels for some of the students), of more than 40 students. The topics treated fall within one of the following fields: geometric group theory, algebraic topology, complex analysis, differential geometry, Lie groups, algebraic geometry. Many of these undergraduate students went on to study mathematics enrolling in Ph.D. programs of other universities.

Services and fundings

  • Referee for several mathematical journals, such as Mathematische Annalen, Ad- vances in Mathematics, Manuscripta Mathematica, Mathematische Zeitschrift, An- nali di Matematica Pura e Applicata, Annali della Scuola Normale Superiore di Pisa, Mathematical Research Letters, Geometry and Topology, Journal of Alge- braic Geometry.

  • Referee for projects of the NSF.

  • MemberofthescientificevaluationcouncilofGRIFGA,”GroupementdeRecherche

    europ ́een Italo-Francais en G ́eom ́etrie Alg ́ebrique.”

  • Member of the committee for the evaluation of Ph.D. theses at the Universities of Milano, Pavia, Roma I, Roma 3, Scuola Normale Superiore di Pisa.

  • Member and local coordinator of the funding project “PRIN” “Spazi di moduli e teoria di Lie”.

    Spoken languages

    Italian (first language), English (fluent), French (good), German (elementary level).

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Selected Publications

[1] L. Migliorini, “A smooth family of minimal surfaces of general type over a curve of genus at most one is trivial”, J. Algebraic Geometry 4, 353-361 (1995).

[2] P. Heinzner, L. Migliorini, M. Polito, “Semistable quotients”, Ann. Scuola Norm. Sup. Pisa, cl.Sci(4) 26 no.2, 233-248(1998).

[3] M.A. de Cataldo, L. Migliorini, “The Chow groups and the motive of the Hilbert schemes of surfaces”, Journal of Algebra 251 (2002), 824-848.

[4] M.A. de Cataldo, L. Migliorini, “The hard Lefschetz theorem and the topology of semismall maps”, Ann. Scient. E ́c. Norm. Su., 4e s ́erie, t.35, 2002, 759-772.

[5] M.A. de Cataldo, L. Migliorini, “The Hodge theory of algebraic maps”, Ann. Scient. E ́c. Norm. Sup.(4)38,(2005) 693-750.

[6] M.A. de Cataldo, L. Migliorini, “The decomposition theorem, perverse sheaves and the topology of algebraic maps”, Bulletin of the Amer.Math.Soc. 46,(2009), 535-633.

[7] M.A. de Cataldo, L. Migliorini, “The perverse filtration and the Lefschetz hyperplane Theorem”, Annals of Math. 171 n.3 (2010) 2089-2113.

[8] M.A. de Cataldo, T. Hausel, L. Migliorini, “The topology of the Hitchin map and the Hodge theory of character varieties ”, Annals of Math. 175 n.3 (2012) 1329-1407.

[9] L. Migliorini, V. Shende, “A support theorem for Hilbert schemes of planar curves”, Journal of the European Mathematical Society 15 (2013), 2353–2367.

[10] L. Migliorini, V. Shende, "Higher discriminants and the topology of algebraic maps" to appear on Algebraic Geometry 2018

 

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