Ada Boralevi
Politecnico di Torino
Corso Duca degli Abruzzi 24,
10129 Torino TO
Phone:
Email:
Homepage:
+39-349-4745789
[email protected]
http://people.sissa.it/∼aborale/
Education
• PhD in Mathematics, Università degli Studi di Firenze, July 2008. Thesis in Algebraic Geometry,
title: Quiver representations and homogeneous vector bundles on flag manifolds. Advisor: Prof. Giorgio
Ottaviani.
• MA in Mathematics, University of California, Los Angeles (UCLA), June 2006.
• Degree in Mathematics (Laurea), 110/110 summa cum laude, Università degli Studi di Firenze,
September 2004. Thesis in Algebraic Geometry, title: The Horrocks-Mumford bundle and its restrictions
to planes. Supervisor: Prof. Giorgio Ottaviani.
• Semester attending the Diplome d’Etudes Approfondies (DEA) “Méthodes Algébriques”,
Université Paris VI, September 2003–February 2004
Employment
Current
• From January 2017: Assistant Professor, Department of Mathematical Sciences, Politecnico di Torino.
Past appointments
• January 2012–January 2013, July 2013–January 2015, & February 2016–January 2017: Postdoctoral
fellow, Geometry and Mathematical Physics Sector, International School for Advanced Studies, Trieste.
• January 2015–January 2016: Postdoctoral fellow, Department of Mathematics and Computer Science,
Technische Universiteit Eindhoven.
• March 2013–June 2013: Postdoctoral fellow, Department of Algebra and Algebraic Geometry, Institute of Mathematics of the Polish Academy of Sciences, Warsaw.
• June 2011–December 2011: Postdoctoral fellow, Dipartimento di Matematica e Informatica, Università degli Studi di Trieste.
• September 2008–May 2011: Visiting Assistant Professor, Mathematics Department, Texas A&M University, College Station.
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Publications
Refereed Journal Articles
1. Truncated modules and linear presentations of vector bundles, with D. Faenzi and P. Lella, to appear in
International Mathematics Research Notices.
2. Orthogonal and unitary tensor decomposition from an algebraic perspective, with J. Draisma, E. Horobeţ,
and E. Robeva, to appear in Israel Journal of Mathematics.
3. Planes of matrices of constant rank and globally generated vector bundles, with E. Mezzetti, Annales de
l’Institut Fourier 65, no. 5 (2015), 2069–2089.
4. Orthogonal bundles and skew-Hamiltonian matrices, with R. Abuaf, Canadian Journal of Mathematics
67 (2015), no. 5, 961–989.
5. Linear spaces of matrices of constant rank and instanton bundles, with D. Faenzi and E. Mezzetti, Advances in Mathematics 248 (2013), 895–920.
6. A note on secants of Grassmannians, Rendiconti dell’Istituto di Matematica dell’Università di Trieste 45
(2013), 67–72.
7. Secants of Lagrangian Grassmannians, with J. Buczyński, Annali di Matematica Pura ed Applicata 190,
4 (2011), 725–739.
8. Sections of homogeneous vector bundles, Journal of Algebra 323 (2010) 2301–2317.
9. Effective results on Picard bundles via M-regularity, with F. Prantil, Le Matematiche 43,1 (2008) 181–203.
10. The Horrocks-Mumford bundle restricted to planes, Collectanea Mathematica 58,1 (2007) 101–117.
Refereed Proceedings
11. On simplicity and stability of the tangent bundle of rational homogeneous varieties, Proceedings of the 2008
Grenoble Summer School “Geometric Methods in Representation Theory”, Séminaires et Congrès,
Société Mathématique de France, 24-II (2012), 273–295.
Book Chapters
12. Weyman’s method for subspace varieties of skew-symmetric tensors, with L.Oeding, in J.M. Landsberg,
Tensors: Geometry and Applications, AMS GSM, vol. 128, (2012), 405–407.
Preprints
13. Uniform determinantal representations, with J. Doornmalen, J. Draisma, M. Hochstenbach and B. Plestenjak, arXiv:1607.04873.
Manuscripts in preparation
- Moduli spaces of framed sheaves on partial desingularizations of toric singularities and quiver varieties, with
F. Sala.
- ED degree of Grassmannians, with J. Draisma, E. Horobet and G. Ottaviani.
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Invited Talks & Other Presentations
Invited Talks
• “Christmas Workshop on Quivers, Moduli Spaces and Integrable Systems”, Genoa, Moduli spaces of
framed sheaves on ( p, q)-toric singularities, December 2016.
• University of Ljubljana, Orthogonal and unitary tensor decomposition from an algebraic perspective, November 2016.
• “Joint Meeting Brazil - Italy in Mathematics”, Orthogonal and unitary tensor decomposition from an
algebraic perspective, Rio de Janeiro, August 2016.
• Institut des Hautes Études Scientifiques, Bures-sur-Yvette, FR, Orthogonal and unitary tensor decomposition from an algebraic perspective, June 2016.
• Conference “Mediterranean Complex Projective Geometry”, Spaces of matrices of constant rank via
cones of morphisms and truncated graded modules, Carry le Rouet, May 2016.
• University of Western Ontario, London, Canada, Orthogonal and unitary tensor decomposition from an
algebraic perspective, April 2016.
• SISSA, Trieste, Orthogonal and unitary tensor decomposition from an algebraic perspective, March 2016.
• Università di Firenze, Un nuovo approccio allo studio dei tensori ortogonalmente decomponibili, February
2016.
• Università di Trieste, Spaces of matrices of constant rank and graded modules, February 2016.
• Technische Universiteit Eindhoven, Orthogonal and unitary tensor decomposition, January 2016.
• “2016 AMS Joint Mathematics Meeting”, Special Session on Nonlinear Algebra, Seattle,Unitarily
decomposable tensors, January 2016.
• “Algebra and Geometry Meeting MAG2015”, Barcelona, Spaces of matrices of constant rank, vector
bundles, and graded modules, December 2015.
• “AMS-EMS-SPM International Meeting 2015”, Special Session on Vector Bundles on Projective Varieties, Oporto, Orthogonal instantons and skew-Hamiltonian matrices, June 2015.
• Intercity Number Theory Seminar, Vrije Universiteit Amsterdam, Linear spaces of matrices of constant
rank, May 2015.
• Technische Universiteit Eindhoven, Spaces of constant rank matrices, July 2014.
• Universidade Estadual de Campinas, Linear spaces of skew-symmetric matrices and instantons, April
2014.
• Universidade Estadual de Campinas, Orthogonal bundles and skew-Hamiltonian matrices, March 2014.
• Christmas Workshop, Università di Milano, Linear spaces of matrices of constant rank, December 2013.
• Università di Torino, Fibrati ortogonali e matrici anti-Hamiltoniane, October 2013.
• Jagellonian University, Krakow, Orthogonal bundles and skew-Hamiltonian matrices, June 2013.
• MIMUW University of Warsaw, Orthogonal bundles and skew-Hamiltonian matrices, April 2013.
• IMPANGA, Warsaw, Spaces of matrices of constant rank and instanton bundles, March 2013.
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• Texas A&M University, Spaces of matrices of constant rank and instantons, February 2013.
• SISSA, Trieste, Spaces of matrices of constant rank and instantons, January 2013.
• UPPA, Pau, Fibrés orthogonaux et matrices skew-Hamiltoniennes, December 2012.
• Institut Fourier, Grenoble, Spaces of matrices of constant rank and instantons, October 2012.
• Università di Trieste, Quiver representations, homogeneous bundles and the BGG resolution, March 2012.
• SISSA, Moduli spaces of orthogonal bundles, January 2012.
• Università di Trieste, Secanti di Grassmanniane e Grassmanniane Lagrangiane, June 2011.
• University of Texas at Austin, Homogeneous vector bundles and quivers, December 2010.
• Colorado State University at Fort Collins, Secant varieties and the Waring problem and Secants of Lagrangian Grassmannians, November 2010.
• UMass Amherst, Homogeneous vector bundles and quivers, October 2010.
• Texas A&M University, Secants of Lagrangian Grassmannians, September 2010.
• Università di Firenze, Secanti di Grassmanniane Lagrangiane, July 2010.
• Università di Trieste, Coomologia di fibrati vettoriali omogenei e rappresentazioni di quivers, June 2009.
• Università di Firenze, Quiver representations and the BGG resolution, June 2009.
• Northeastern University, Boston, Cohomology of homogeneous vector bundles via quiver representations,
April 2009.
• Texas A&M University, Simplicity and stability of tangent bundles on rational homogeneous varieties,
March 2009.
• Conference “Geometric Methods in Representation Theory”, Institut Fourier, Grenoble, Quivers and
homogeneous vector bundles on flag manifolds, June 2008.
• Conference “Giornate di Geometria Algebrica e argomenti correlati IX”, Levico Terme, Fibrati vettoriali omogenei su varietà di bandiera e rappresentazioni di quivers, May 2008.
• Università di Firenze, Rappresentazioni di quivers e fibrati omogenei, May 2008.
• Conference “Progressi Recenti in Geometria Reale e Complessa”, Levico Terme, Il fibrato di HorrocksMumford ristretto ai piani, October 2006.
• Workshop “Giornata Informale di Geometria Algebrica”, Firenze, Risoluzioni per le restrizioni del
fibrato di Horrocks-Mumford ai piani, April 2005.
Contributed Talks (Accepted talk proposals)
• Conference “Moduli Spaces in Algebraic Geometry and Mathematical Physics”, Chern Institute of
Mathematics, Tianjin, Orthogonal instantons and skew-Hamiltonian matrices, September 2015.
• Conference “VBAC 2013, Vector Bundles on Algebraic Curves”, SISSA, Trieste, Spaces of matrices of
constant rank and instanton bundles, June 2013.
• Conference “MEGA, Effective Methods in Algebraic Geometry”, Frankfurt, Spaces of matrices of constant rank and instanton bundles, June 2013.
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• Workshop “Syzygies in Berlin”, Spaces of matrices of constant rank and instanton bundles, May 2013.
• Workshop on “Moduli Spaces and Mathematical Physics”, CIMAT, Guanajuato, Orthogonal bundles,
skew-Hamiltonian matrices, and determinantal varieties, January 2013.
• Workshop on “Invariant Theory and Projective Geometry”, CIRM, Trento, Linear systems of skewsymmetric matrices of constant rank and instanton bundles, September 2012.
• Conference “GAeL XVII, Géométrie Algébrique en Liberté”, Leiden, Simplicity and stability of tangent
bundles on rational homogeneous varieties, June 2009.
• Conference “GAeL XVI, Géométrie Algébrique en Liberté”, Aranjuez, Homogeneous vector bundles and
quiver representations, April 2008.
Other Presentations (Contributions to the following working seminars:)
• SMUGA, Working seminar in Algebraic Geometry, Warsaw
• Geometry Seminar Trieste-Udine
• SISSA Running Seminar in Geometry
• Texas A&M University Working Seminar in Geometry
• Texas A&M University Students/Postdocs Working Geometry Seminar
Teaching & Supervising Experience
Instructor
- A.A. 2014-2015, Università degli Studi di Trieste: Matematica per il CdL Farmacia
- A.A. 2013-2014, Università degli Studi di Trieste: Matematica per il CdL Farmacia
- Spring 2011, Texas A&M University (TAMU): Business Mathematics 1 - Math 141
- Fall 2010, TAMU: Business Mathematics 1 - Math 141 (2 sections)
- Spring 2010, TAMU: Calculus I - Math 151
- Fall 2009, TAMU: Calculus I - Math 151 (2 sections)
- Spring 2009, TAMU: Linear Algebra - Math 304
- Fall 2008, TAMU: Business Mathematics 1 - Math 141 (2 sections)
Teaching Assistant
- A.A. 2014-2015, Mastermath, joint Dutch Universities Master program: Commutative Algebra.
- A.A. 2011-2012, Università degli Studi di Trieste: Geometria 1 per il CdL Matematica e Fisica
- A.A. 2006-2007, Università degli Studi di Firenze: Geometria per il CdL Ingegneria Meccanica
- Spring 2006, UCLA: Calculus of Several Variables - Math 32a
- Spring 2006, UCLA: Introduction to Topology - Math 121
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Supervisor
- Co-supervisor, BS-level undergraduate thesis, Università degli Studi di Trieste, CdL Matematica.
Student Elia Rizzo, thesis titled “Esempi di varietà omogenee”, defended in December 2011.
Organizational Experience
Seminars
- Co-organizer, Geometry Seminar Trieste-Udine, Università degli Studi di Trieste and Università di
Udine, September 2011-January 2013, bi-weekly meetings.
- Co-organizer, “Algebra, Combinatorics and Algebraic Geometry Seminar”, TAMU, Spring 2011,
weekly meetings.
- Co-organizer, Graduate Student Seminar Colloquiando, Dipartimento “U.Dini”, Università degli Studi
di Firenze, March–June 2008, weekly meetings.
Schools and workshops
- Part of the organizing committee of “SSiEG - Summer School in Enumerative Geometry”, to be held
at SISSA, Trieste, July 2017.
- Part of the organizing committee of “MEGA 2017 – Effective Methods in Algebraic Geometry”, to be
held in Nice–Sophia Antipolis University, June 2017.
- “Vector Bundles Days, Pau-Trieste Workshop on Vector Bundles and Related Topics”, with D. Faenzi
(UPPA), E. Mezzetti (Trieste), and J. Vallès (UPPA), held in Pau, April 2013.
- “Vector Bundles Days II, Pau-Trieste Workshop on Vector Bundles and Related Topics, On the occasion of Emilia Mezzetti’s 60th birthday”, with V. Beorchia (Trieste), P. De Poi (Udine), D. Faenzi
(UPPA), D. Portelli (Trieste), and J. Vallès (UPPA), held in Trieste, January 2014.
- Summer School “An interdisciplinary approach to tensor decomposition”, organized with A. Bernardi
(Bologna) and E. Postinghel (Leuven), a held at CIRM-FBK, Trento, in July 2014. Courses by JM
Landsberg, B. Mourrain, and K. Ranestad.
Scholarships, Certificates, Grants
• 2015: part of J. Draisma (TU Eindhoven, NL)’s research project Vidi, funded by Netherlands Organization for Scientific Research.
• 2014–present: part of the research project FRA 2013 (Finanziamento Ricerca di Ateneo) titled “Geometria e topologia delle varietà”, Università degli Studi di Trieste. Director of the project Prof.
Mecchia (Univ. Trieste).
• 2013-present: part of the research project PRIN (Progetto di Ricerca di Interesse Nazionale) titled
“Geometria delle varietà algebriche”, Italian National Government Funding. Directors of the project
Prof. Verra (Università Roma 3) and Prof. Bruzzo (SISSA, Trieste).
• 2012–2013: part of the research project FRA 2011 titled “Geometria e topologia delle varietà”, Università degli Studi di Trieste. Director of the project Prof. Mezzetti.
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• 2011–2012: part of the research project PRIN titled “Geometria delle varietà algebriche e dei loro
spazi di moduli”, Italian National Government Funding. Directors of the project Prof. Verra (Università Roma 3) and Prof. Bruzzo (SISSA, Trieste).
• 2009–2010: part of the research project PRIN titled “Proprietà geometriche delle varietà reali e complesse”, Italian National Government Funding. Director of the project Prof. Ancona (Università degli
Studi di Firenze).
• 2007–2008: part of the research project PRIN titled “Proprietà geometriche delle varietà reali e complesse”, Italian National Government Funding. Director of the project Prof. Gentili (Università degli
Studi di Firenze).
• University of Florence PhD Scholarship, January 2005–January 2008.
• Scholarship funded by the joint program “Firenze-UCLA” organized by UCLA and Università degli
Studi di Firenze for Graduate Study at the UCLA Mathematics Department, August 2005–June 2006.
• Erasmus Scholarship from Università degli Studi di Firenze to attend a semester of Graduate courses
at the DEA Méthodes Algébriques, Université Paris VI, September 2003–February 2004.
Service
Professional
- Referee, Journal of Pure and Applied Algebra, International Mathematics Research Notices, Rendiconti del Circolo Matematico di Palermo, Bollettino dell’Unione Matematica Italiana.
- Reviewer for the American Mathematical Society.
Professional societies
- Unione Matematica Italiana
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (Istituto Nazionale
di Alta Matematica)
Additional Conferences & Schools attended
◦ Geometria delle Varietà Algebriche, Conference, Levico Terme, Jun 2016.
◦ 2015 Summer Research Institute on Algebraic Geometry, Conference, University of Utah, Salt Lake City,
July 2015.
◦ MEGA, Effective Methods in Algebraic Geometry, Conference, Trento, June 2015.
◦ Symmetries of Kähler manifolds, dynamics and moduli spaces, Workshop, SISSA, Trieste, September 2014.
◦ Derived Categories, School (courses by Gaitsgory, Krause, Kutznetsov, Toda), Nantes, June 2014
◦ Giornate di Geometria Algebrica e argomenti correlati XII, Conference, Torino, June 2014
◦ Homage to Corrado Segre, Conference, Torino, November 2013.
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◦ Classification of Algebraic Varieties and Related Topics, Conference, Cetraro, September 2013.
◦ Moduli Spaces and Mathematical Physics, School, CIMAT, Guanajuato, January 2013.
◦ Invariant Theory and Projective Geometry, School (courses by Manivel and Ottaviani), CIRM, Trento,
September 2012.
◦ Genova-Torino-Milano Seminar, Torino, June 2012.
◦ Arrangements in Pyrénées, School and Workshop, Pau, June 2012.
◦ Derived categories in Algebraic Geometry, Workshop, Dijon, May 2012.
◦ On Tropical and Toric Geometry, School and Workshop (courses by Di Rocco and Mikhalkin), CIRM,
Trento, September 2011.
◦ Texas Algebraic Geometry Seminar TAGS 2011, Rice University, Houston, April 2011.
◦ Classical Algebraic Geometry, Workshop, Roma, February 2011.
◦ 44th Texas Geometry and Topology Conference TGTC, Texas A&M University, College Station, November
2010.
◦ IMPANGA Summer school on Algebraic Geometry 2010, Institute of Mathematics of the Polish Academy
of Sciences, Bedlewo, July 2010.
◦ Complex Algebraic Geometry, Conference, Institut Henri Poincaré, Paris, June 2010.
◦ Geometry of tensors and applications, School (courses by Landsberg, Ottaviani, Weyman), Nordfjordeid,
June 2010.
◦ Texas Algebraic Geometry Seminar TAGS 2010, University of Texas at Austin, May 2010.
◦ Western Algebraic Geometry Seminar WAGS Fall 2009, UCLA, Los Angeles, October 2009.
◦ Degenerations, Projective Varieties and Interpolation Theory, SMI School (courses by Ciliberto and Miranda), Cortona, July 2009.
◦ VBAC 2009, Vector Bundles on Algebraic Curves, Conference, Berlin, June 2009.
◦ GAeL XVII, Géométrie Algébrique en Liberté, School (courses by Farkas, Müller-Stach, Sottile), Leiden,
June 2009.
◦ Texas Algebraic Geometry Seminar TAGS 2009, Texas A&M University, College Station, May 2009.
◦ 41st Texas Geometry and Topology Conference, University of Houston, February 2009.
◦ Classical Algebraic Geometry Today, Workshop, MSRI, Berkeley, January 2009.
◦ 40th Texas Geometry and Topology Conference, University of Texas at Austin, October 2008.
◦ Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas, Workshop,
AIM, Palo Alto, July 2008.
◦ Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas, School
(courses by Landsberg, Lim, Morton), MSRI, Berkeley, July 2008.
◦ Aspects of Moduli, Conference, Centro De Giorgi, Pisa, June 2008.
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◦ GAeL XVI, Géométrie Algébrique en Liberté, School (courses by Demailly, Huybrechts, Vistoli), Aranjuez, April 2008.
◦ Geometry of Special Varieties, School and Workshop (courses by Ciliberto and Russo), CIRM, Trento,
September 2007.
◦ P.R.A.G.M.A.T.I.C. 2007, Fourier-Mukai transforms, generic vanishing and regularity, School (courses by
Pareschi and Popa), Catania, July 2007.
◦ Algebraic Geometry in Higher Dimensions, Conference, Levico Terme, June 2007.
◦ Interactions with Algebraic Geometry, Conference, Firenze, May 2007.
◦ Geometria proiettiva e birazionale delle varietà algebriche, School (courses by Ionescu, Mella, Ottaviani),
Gargnano, April 2007.
◦ Vector Bundles and Low Codimensional Subvarieties, School and Workshop (courses by Ellia and MiróRoig), CIRM, Trento, September 2006.
◦ AGaFe 2005, Geometry of Algebraic Varieties, Conference, Ferrara, June 2005.
◦ Algebraic Geometry and Categories, Conference, Nice, June 2005.
◦ Journées de Géométrie Algébrique, Conference, Lille, May 2005.
Personal Information
• Citizenship: Italian (Born: Florence, Italy)
• Date of birth: September 17th, 1981
• Languages: Italian (native speaker), English (excellent), French (excellent), German (elementary),
Spanish (elementary).
Certificate of Proficiency in English, University of Cambridge, UK, December 1998.
• Computer skills: LATEX, Maple, Macaulay2, LiE
Last updated: February 7, 2017
