Alex Massarenti
Professor Adjunto I - UFF
Universidade Federal Fluminense, UFF
Instituto de Matemática
Rua Mário Santos Braga, 24020-140, Niterói
Rio de Janeiro, Brazil
T +442198566325
u +4421589653254
B [email protected]
Í http://w3.impa.br/ massaren/
Born in Portomaggiore (Italy), on May 9th, 1985
Education
2009–2013 Ph.D. in Mathematics (Geometry), International School for Advanced Studies (SISSAISAS), July 5, 2013, Trieste.
Thesis on: ”Biregular and Birational geometry of Algebraic Varieties”, awarded the SISSA Lutman
Prize 2014 for the Best Ph.D. Thesis in Mathematics.
Advisor: Prof. Massimiliano Mella.
Internal Advisor: Prof. Barbara Fantechi.
2007–2009 Master Degree (Laurea Specialistica) in Mathematics, Università di Ferrara, July 17,
2009, 110/110 cum Laude.
Thesis on: ”VSP - Varieties of Sums of Powers”.
Advisor: Prof. Massimiliano Mella.
2004–2007 Bachelor Degree (Laurea Triennale) in Mathematics, Università di Ferrara, July 20,
2007, 110/110 cum Laude.
Thesis on: ”Elliptic Curves”.
Advisor: Prof. Philippe Ellia.
1999–2004 High School Degree, Liceo Scientifico T.L. Civita, June 26, 2004, Codigoro (Ferrara),
100/100 cum Laude.
Past Employment
2013–2015 Post-doctoral fellow (Pos-doutorado de Excelência), National Institute of Pure and
Applied Mathematics IMPA, Rio de Janeiro, Algebraic Geometry group.
Present Position
2015–Present Professor Adjunto I, Universidade Federal Fluminense UFF, Niterói, Rio de Janeiro.
Scientific Activity
The branch of mathematics in which I am most interested is Algebraic Geometry.
- Research interests: Birational geometry of projective varieties. Varieties of Sums of Powers. Uniruled,
rationally connected and Fano varieties. Moduli spaces and moduli stacks of curves and stable maps. Mori
Dream Spaces, log Fano and weak Fano varieties.
- Other activities: I am a reviewer for MathSciNet.
- Publications and Preprints:
1. C. Araujo, A. Massarenti, Explicit log Fano structures on blow-ups of projective spaces, submitted,
(arXiv:1505.02460v1).
2. M. Bolognesi, A. Massarenti, Moduli of abelian surfaces, symmetric theta structures and theta characteristics, submitted, (arXiv:1409.5033v1).
3. B. Fantechi, A. Massarenti, On the rigidity of moduli of curves in arbitrary characteristic, submitted,
1/5
(arXiv:1407.2284v2).
4. A. Massarenti, M. Mella, On the automorphisms of Hassett’s moduli spaces, submitted, (arXiv:1307.6828v2).
5. A. Massarenti, Generalized varieties of sums of powers, to appear on Bulletin of the Brazilian Mathematical Society, (arXiv:1401.2059v1).
6. A. Massarenti, M. Mella, On the automorphisms of moduli spaces of curves, Springer Proceedings in
Mathematics and Statistics, 2014, Vol. 79, 149-168, (arXiv:1305.6182v2).
7. A. Massarenti, The automorphism group of M g,n , Journal of the London Mathematical Society,
2014, Vol. 89, 131-150, (arXiv:1110.1464v1).
8. S. Marchesi, A. Massarenti, Varieties connected by chains of lines, Geometriae Dedicata, 2014, Vol
168, Issue 1, 61-68, (arXiv:1106.0124v1).
9. A. Massarenti, M. Mella, Birational aspects of the geometry of varieties of sums of powers, Advances
in Mathematics, 2013, Vol. 243, pp. 187-202, (arXiv:1010.1707v2).
10. A. Massarenti, E. Raviolo, On the rank of n × n matrix multiplication, Linear Algebra and its
Applications, Vol 438, Issue 11, 2013, 4500-4509, (arXiv:1211.6320v2).
11. S. Marchesi, A. Massarenti, S. Tafazolian, Covered by lines and conic connected varieties, Le Matematiche, Vol. LXVI, 2011, Fasc. II, pp. 137-151, (arXiv:1105.5918v2), (Pragmatic 2010).
Students
2015–Present Ph.D. Thesis, Rick Antônio Rischter, Log Fano varieties and Mori Dream Spaces, National
Institute of Pure and Applied Mathematics, IMPA, Rio de Janeiro.
Advisor: Carolina Araujo,
Co-Advisor: Alex Massarenti.
Teaching
- Calculus 2B (UFF - November 2015 - March 2016).
- Ph.D. Course, Topics in Algebraic Geometry: Cox Rings (IMPA, January - February 2015).
-
-
Topics: Mori Dream Spaces and Cox Rings. Weak Fano and log Fano varieties. Representations of semi-simple Lie
algebras and Weyl groups. Secant varieties of rational normal curves. Canonical and terminal singularities. Log
Fano varieties obtained by blowing-up points in Pn . Moduli spaces of curves, M 0,n is not a Mori Dream Space for
n > 133.
Ph.D. Course, Algebraic Geometry I (IMPA, August - November 2014).
Topics: Affine and projective varieties, Hilbert’s nullstellensatz, Zariski’s topology, Bézout’s theorem. Morphisms
and rational maps. Singularities of algebraic varieties. Projective curves. Blow-ups, resolutions of singularities of
curves. Veronese and Segre varieties. Grassmannians. Twenty-seven lines in a smooth cubic surface and lines in
hypersurfaces of small degree. Theorems on the dimension of the fibers. Secant varieties, rational normal scrolls.
Line bundles and divisors. Riemann-Roch theorem for smooth curves.
Tutorial, Algebraic Geometry (Ph.D. Course) (SISSA, November - December, 2011).
Tutorial, Projective and Algebraic Geometry (Università di Ferrara, January - March, 2009).
Tutorial, Rings and Fields Theory (Università di Ferrara, October - December, 2008).
Tutorial, Projective and Differential Geometry (Università di Ferrara, January - March, 2008).
Tutorial, Algebraic Topology (Università di Ferrara, October - December, 2007).
Visits
-
March - April, 2012 : ETH in Zürich, visiting Prof. Rahul Pandharipande.
March - April, 2013 : Institut de Mathématiques de Jussieu in Paris, visiting Prof. Alessandro Chiodo.
May - June, 2014 : Université de Rennes 1 in Rennes, visiting Prof. Michele Bolognesi.
October 5-12, 2014 : UFMJ - Universidade Federal de Minas Gerais in Belo Horizonte, visiting Prof.
Maurício Corrêa.
- December 2-5, 2014 : Università di Torino, visiting Prof. Cinzia Casagrande.
Talks
{ Birational geometry of Varieties of Sums of Powers
2/5
{
{
{
{
{
{
{
{
{
{
{
{
-
March 28, 2009, SISSA (Trieste).
The automorphism group of M g,n
October 23, 2011, SISSA (Trieste).
February 7, 2012, Università di Ferrara.
February 17, 2012, TULFS VII - A.G. in Trieste-Udine-Ljubljana-SISSA-Ferrara (Trieste).
March 16, 2012, ETH (Zürich).
May 25, 2012, Giornate di Geometria Algebrica ed Argomenti Correlati XI (Centro Ennio De Giorgi - SNS,
Pisa).
June 21, 2012, GAeL XX 2012 - Géométrie Algébrique en Liberté (Institut Fourier, Grenoble).
Kontsevich’s moduli spaces, Gromov-Witten invariants and quantum cohomology
May 2, 2012, UZH - Institut für Mathematik (Zürich).
The 2-Secant varieties of Veronese varieties
July 4, 2012, Tensors: Waring problems and Geometric Complexity Theory (Cortona).
On the automorphisms of Hassett’s moduli spaces
April 18, 2013, Institut de Mathématiques de Jussieu (Paris).
June 14, 2013, Recent trends in the geometry of moduli spaces of curves (SISSA, Trieste).
July 4, 2013, ACA 2013 - Arithmetic of algebraic curves (Málaga).
On the automorphisms of moduli spaces of curves
September 25, 2013, IMPA (Rio de Janeiro).
October 8, 2013, UFF - Universidade Federal Fluminense (Rio de Janeiro).
October 10, 2014, UFMJ - Universidade Federal de Minas Gerais (Belo Horizonte).
March 26, 2015, UFRJ - Universidade Federal do Rio de Janeiro (Rio de Janeiro).
January 5, 2015, Institut Fourier (Grenoble).
April 6, 2015, Moduli spaces and enumerative geometry, IMPA (Rio de Janeiro).
August 20, 2015, PUC - Pontifícia Universidade Católica, (Rio de Janeiro).
The rigidity of M 0,n in positive characteristic
February 21, 2014, LEGAL 2014 - Liberdade em Geometria Algébrica (Teresópolis, Rio de Janeiro).
Varieties of Sums of Powers
March 28, 2014, Colóquio de Geometria e Aritmética (UFF - Universidade Federal Fluminense, Rio de
Janeiro).
Mori Dream Spaces obtained by blowing-up points on a smooth quadric hypersurface
July 29, 2014, XXIII Escola de Álgebra (Universidade Estadual de Maringá, Maringá, Brazil).
Weak Fano and log Fano varieties obtained by blowing-up points in Pn
September 2, 2014, UFF - Universidade Federal Fluminense (Rio de Janeiro).
September 17, 2014, IMPA (Rio de Janeiro).
October 23, 2014, UNICAMP - Universidade Estadual de Campinas (Campinas, Brazil).
December 3, 2014, Università di Torino.
Explicit log Fano structures on blow-ups of projective spaces
June 4, 2015, II Latin American School of Algebraic Geometry and Applications (II ELGA), Cabo Frio
(Brazil).
Automorphisms of Kontsevich moduli spaces
June 17, 2015, AGaFe - A conference in honour of Philippe Ellia on his 60th birthday, Università di Ferrara.
July 29, 2015, 30◦ Colóquio Brasileiro de Matemática (IMPA, Rio de Janeiro).
Mori Dream Spaces and classical projective geometry
July 8, 2015, SISSA (Trieste).
Attended Courses, Schools and Workshops (short selection)
- School: "Summer school on Geometric and Algebraic Methods with Applications in Physics".
University of Antwerp, Antwerp (Belgium). July 14 - July 26, 2008.
- PhD Course: "Geometry of Varieties in Spaces of Tensors".
Università di Firenze, Firenze (Italy). May 25 - May 28, 2009.
- School: "School and Workshop on Hodge Theory and Algebraic Geometry".
3/5
Università di Trento, Trento (Italy). August 31 - September 5, 2009.
- Workshop: "Giornate di Geometria Algebrica ed Argomenti Correlati X".
Feltrinelli Palace of Gargnano, Gargnano (Italy). May 25 - May 29, 2010.
- School: "School and Workshop on Local Rings and Local Study of Algebraic Varieties".
ICTP, Trieste (Italy), May 31 - June 11, 2010.
- School: "Summer School on Hodge Theory".
ICTP, Trieste (Italy). June 14 - July 2, 2010.
- School: "School (and Workshop) on the Minimal Model Program and Shokurov’s ACC Conjecture".
Università di Trento, Trento (Italy). July 5 - July 10, 2010.
- School: "P.R.A.G.MAT.I.C. 2010 - Mori Theory in a Variety of Flavors".
Università di Catania, Catania (Italy). August 30 - September 18, 2010.
- School: "Young Researchers in Arithmetic and Algebraic Geometry".
University of Mainz, Mainz (Germany). October 04 - October 07, 2010.
- School: "School on Moduli Spaces".
Newton Institute for Mathematical Sciences, Cambridge (United Kingdom). January 5 - January 14, 2011.
- Workshop: "Classical Algebraic Geometry".
Università La Sapienza, Rome (Italy). February 9 - February 11, 2011.
- School: "Moduli of Curves and Gromow-Witten theory".
Institut Fourier, Grenoble (France). June 20 - July 1, 2011.
- School: "GAeL XIX 2011 - Géométrie Algébrique en Liberté".
Berlin Mathematical School, Berlin (Germany). July 18 - July 22, 2011.
- School: "Curves of low degrees in Fano varieties".
Università Tor Vergata, Rome (Italy). May 8 - May 10, 2012.
- Workshop: "Giornate di Geometria Algebrica ed Argomenti Correlati XI".
Centro Ennio De Giorgi - Scuola Normale Superiore, Pisa (Italy). May 23 - May 26, 2012.
- School: "GAeL XX 2012 - Géométrie Algébrique en Liberté".
Institut Fourier, Grenoble (France). July 18 - July 22, 2012.
- School: "Tensors: Waring problems and Geometric Complexity Theory".
Palazzone di Cortona, Cortona (Italy), July 2 - July 14, 2012.
- School: "Geometry of Sheaves in Low Dimensions".
Centro Stefano Franscini, Ascona (Switzerland), January 21 - January 25, 2013.
- School: "LEGAL 2014 - Liberdade em Geometria Algébrica".
Teresópolis, Rio de Janeiro (Brazil). February 17 - February 22, 2014.
- School: "GAeL XXII 2014 - Géométrie Algébrique en Liberté".
SISSA, Trieste (Italy). June 23 - June 27, 2014.
- School: "XXIII Escola de Álgebra".
UEM- Universidade Estadual de Maringá, Maringá (Brazil). July 27 - August 1, 2014.
- School: "Géométrie Algébrique et Géométrie Complexe".
Centre international de rencontres mathématique, Marseille (France). November 24 - November 28, 2014.
- School and Workshop: "Moduli Spaces and Enumerative Geometry".
IMPA, Rio de Janeiro. April 6 - April 10, 2015.
- School and Workshop: "Modular Forms and Geometry of Modular Varieties".
IMPA, Rio de Janeiro. May 4 - May 8, 2015.
- School and Workshop: "Workshop on Higher Dimensional Algebraic Geometry".
IMPA, Rio de Janeiro. May 18 - May 22, 2015.
- School and Workshop: "Rational points".
IMPA, Rio de Janeiro. May 25 - May 29, 2015.
- School and Workshop: "II Latin American School of Algebraic Geometry and Applications (II ELGA)".
Cabo Frio, Brazil. June 1 - June 12, 2015.
4/5
Organizational Experience
- Conference: "Mirror Symmetry and Spin Curves".
Organizers: S. Boissiére, A. Chiodo, É. Mann, A. Massarenti.
At: Palazzone di Cortona (Italy).
April 28 - April 30, 2014.
Languages
- Mother tongue: Italian.
- Other languages:
Understanding
Listening
Reading
Speaking
Spoken interactionSpoken production
English
C1
Advanced
C1
Advanced
C1
Portuguese C1 Advanced C1 Advanced B2
French
B2Upper IntermediateB2Upper IntermediateB1
Advanced
C1
Advanced
Upper Intermediate
B2
Upper Intermediate
Intermediate
B1
Intermediate
Writing
C1
Advanced
B2Upper Intermediate
B1
Intermediate
Computer skills
-
Good knowledge of Windows, Linux and Mac OS X operative systems.
Very good knowledge of LaTeX.
Good knowledge of MacAulay2 and Bertini.
Good knowledge of Matlab, Mathematica and Maple.
5/5