Dottorato in MATEMATICA

email: viviani@mat.uniroma2.it

(1) EDUCATION

-- MASTER DEGREE at University of Pisa.
Thesis defended on 12 July 2001. Grade: 110/110 cum laude
Title of the thesis: Ramification properties of radical extensions of the rationals.
Advisor: prof. R. Dvornicich.
-- DIPLOMA at SCUOLA NORMALE SUPERIORE of Pisa.
Thesis defended on November 2002. Grade: 70/70 cum laude.
-- PHD DEGREE at University of Rome II.
Thesis defended on 25th of May 2007.
Title of the thesis: Deformations of restricted simple Lie algebras.
Advisor: prof. R. Schoof.

(2) POSITIONS

--POST-DOC POSITION at Mittag-Leffler Institute of Stockholm, September 2006--June 2007.

-- POST-DOC POSITION at the H\"umboldt University of Berlin, September 2007--December 2008.

-- Member of the research center CMUC (=Centro de Matematica da Universidade de Coimbra), University of Coimbra (Portugal), 2009--2014.

-- RICERCATORE (=research assistant) at the Roma Tre University, 2009--2014.

-- PROFESSORE ASSOCIATO (=associate professor) at the Roma Tre University, 2014--2023.

-- PROFESSORE ORDINARIO (=full professor) at the University of Roma Tor Vergata 2023--present.


(3) FELLOWSHIPS, AWARDS and GRANTS

-- 2007: Post-Doc at the Mittag-Leffler Institute, Stockholm (Sweden).

-- 2008-2009: Post-Doc at the H\"umboldt University of Berlin (Germany).

-- 2009-2014: Research Grant Ci\^encia 2008 from the Funda\c c\~ao para a Ci\^encia e a Tecnologia (Portugal).

-- 2011-2014: Principal Investigador of the project ``Espa\c cos de moduli em geometria alg\'ebrica'' funded by the FCT (=Funda\c c\^ao para a Ci\^encia e a Tecnologia) of the Ministry of Education and Research of Portugal (total budget \euro{ 80.392}).

-- 2013-2018: Scientific coordinator of the Research Unit of Roma Tre of the FIRB project ``Spazi di moduli e applicazioni'' funded by MIUR, Ministry of Education, University and Research of Italy (the total budget for the Research Unit of Roma Tre is \euro{ 178.749}).

-- 2012: I obtained the Italian National Scientific Qualification to become Professor of \emph{II fascia} (=Associate Professor), which is valid for 6 years.

-- 2012: I obtained the Italian National Scientific Qualification to become Professor of \emph{I fascia} (=Full Professor), which is valid for 6 years.

-- 2014: I was awarded to the Guido Fubini prize for young italian geometers.

-- 2019: I obtained the Italian National Scientific Qualification 2018/2020 to become Professor of \emph{I fascia} (=Full Professor), which is valid until 04/09/2025.


(4) PAPERS

-- The line bundles on the moduli stack of principal bundles on families of curves. (joint with R. Fringuelli). Proc. Edinb. Math. Soc. (2) 68 (2025), no. 1, 80--127.

-- Slope inequalities for KSB-stable and K-stable families (joint with G. Codogni, L. Tasin). Proc. London Math. Society 126 (2023), 1394--1465.

-- The Picard group of the universal moduli stack of principal bundles on pointed smooth curves II (joint with R. Fringuelli).
Annali della Scuola Normale Superiore di Pisa 24 (2023), 367--447.

-- On the first steps of the minimal model program for the moduli space of stable pointed curves (joint with G. Codogni, L. Tasin).
Journal of the Institute of Mathematics of Jussieu 22 (2023), 145--211.

-- Tropicalization of the universal Jacobian} (joint with M. Melo, S. Molcho, M. Ulirsch. \'Epijournal de G\'eom\'etrie Alg\'ebrique, Volume 6 (2022), Article Nr. 15.

-- The Picard group of the universal moduli stack of principal bundles on pointed smooth curves (joint with R. Fringuelli). J. of Topology 15 (2022), 2065--2142.

-- On some modular contractions of the moduli space of stable pointed curves (joint with G. Codogni, L. Tasin). Algebra \& Number Theory 15-5 (2021), 1245--1281.

-- A support theorem for Hilbert schemes of planar curves, II. (joint with L. Migliorini, V. Schende). Compositio Math. 157 (2021), 835--882.

-- Effective cycles on the symmetric product of a curve, II: the Abel-Jacobi faces (joint with F. Bastianelli, A. Kouvidakis, A.F. Lopez). Rend. Lincei Mat. Appl. 31 (2020), 839--878.

-- Moduli and periods of supersymmetric curves (joint with G. Codogni). Advances in Theoretical and Mathematical Physics, Vol. 23, No. 2 (2019), pp. 345--402.

-- Effective cycles on the symmetric product of a curve, I: the diagonal cone. (joint with F. Bastianelli, A. Kouvidakis, A.F. Lopez, with an Appendix of B. Moonen).
Trans. Amer. Math. Soc. 372 (2019), no. 12, 8709--8758.

-- Fourier-Mukai and autoduality for compactified Jacobians II. (joint with M. Melo, A. Rapagnetta). Geometry and Topology 23-5 (2019), 2335--2395.

-- Fourier-Mukai and autoduality for compactified Jacobians I. (joint with M. Melo, A. Rapagnetta). J. Reine Angew. Math. 755 (2019), 1-65.

-- The singularities and birational geometry of the universal compactified Jacobian (joint with S. Casalaina-Martin, J. L. Kass).
Algebraic Geometry 4 (3) (2017), 353--393.

-- Fine compactified Jacobians of reduced curves (joint with M. Melo, A. Rapagnetta). Trans. Amer. Math. Soc. 369 (2017), no. 8, 5341--5402.

-- Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves (joint with S. Cacciola, A. F. Lopez). Michigan Math. J. 65 (2016), no. 3, 533--546.

-- The local structure of compactified Jacobians (joint work with S. Casalaina-Martin, J. L. Kass). Proc. London Math. Soc. 110 (2015), 510--542.

-- Geometric invariant theory for polarized curves (joint with G. Bini, F. Felici, M. Melo). Lecture Notes in Mathematics 2122 (2014).

-- A tour on Hermitian symmetric manifolds. Combinatorial Algebraic Geometry (Levico Terme, Italy 2013), Editors: Sandra Di Rocco, Bernd Sturmfels. Lecture Notes in Mathematics 2108, pp. 149--239 (2014).

-- The Picard group of the compactified universal Jacobian (joint with M. Melo). Documenta Mathematica 19 (2014), 457--506.

-- Tropicalizing vs Compactifying the Torelli morphism. Tropical and Non-Archimedean Geometry (Proceedings of the Conference Tropical and Non Archimedean Geometry, Bellairs Research Institute, May 2011), Contemp. Math. 605 (2013), 181--210.

-- The geometry and combinatorics of cographic toric face rings (joint with S. Casalaina-Martin, J. L. Kass). Algebra Number Theory 7 (2013), no. 8, 1781--1815.

-- Tropical Teichm\"uller and Siegel spaces (joint with M. Chan, M. Melo). Algebraic and Combinatorial Aspects of Tropical Geometry (Proceedings of CIEM workshop on tropical geometry, Castro Urdiales, December 2011), Contemp. Math. 589 (2013), 45--85.

-- Comparing perfect and 2nd Voronoi decompositions: the matroidal locus (joint work with M. Melo). Math. Ann. 354 (2012), no. 4, 1521–-1554.

-- Restricted infinitesimal deformations of restricted simple Lie algebras. J. Algebra Appl. 11 (2012), no. 5, 1250091, 19 pp.

-- Fine compactified Jacobians (joint work with M. Melo). Math. Nachr. 285 (2012), no. 8-9, 997--1031.

-- On the birational geometry of the universal Picard variety (joint work with G. Bini and C. Fontanari). Int. Math. Res. Not. IMRN 2012, no. 4, 740--780.

-- On GIT quotients of Hilbert and Chow scheme of curves (joint work with G. Bini, M. Melo). Electron. Res. Announc. Math. Sci. 19 (2012), 33--40.

-- The Chow ring of the stack of cyclic covers of the projective line (joint with D. Fulghesu). Ann. Inst. Fourier (Grenoble) 61 (2011), no. 6, 2249--2275.

-- Torelli theorem for stable curves (joint with L. Caporaso). J. Eur. Math. Soc. (JEMS) 13 (2011), no. 5, 1289--1329.

-- On the tropical Torelli map (joint work with S. Brannetti, M. Melo). Advances in Mathematics 226 (2011), 2546-2586.

-- Torelli theorem for graphs and tropical curves (joint work with L. Caporaso). Duke Mathematical Journal Vol.153, no. 1 (2010), 129--171.

-- Simple finite group schemes and their infinitesimal deformations. Rend. Sem. Mat. Univ. Politec. Torino Vol. 68 (2010), 171--182.

-- A note on families of hyperelliptic curves (joint work with S. Gorchinskiy). Archiv der Mathematik 92 (2009), 119-128.

-- Deformations of the restricted Melikian Lie algebra. Communications in Algebra 37 (2009), no. 7, 1850--1872.

-- Infinitesimal deformations of simple restricted Lie algebras II. Journal of Pure and Applied Algebra 213 (2009), 1702-1721.

-- Cohomological support loci for Abel-Prym curves (joint work with S. Casa\-laina-Martin and M. Lahoz). Le Matematiche LXIII (2008), 205--222.

-- Infinitesimal deformations of simple restricted Lie algebras I. Journal of Algebra 320 (2008), 4102--4131.

-- Deformazioni di algebre di Lie semplici ristrette. Matematica nella Societ\`a e nella Cultura 1 (2008), no. 2, 371--374.

-- Picard group of moduli of hyperelliptic curves (joint work with S. Gorchinskiy). Mathematische Zeitschrift 258 (2008), 319--331.

-- Restricted simple Lie algebras and their infinitesimal deformations. From Lie Algebras to Quantum Groups (Proceedings of the Conference "From Lie Algebras to Quantum groups", Coimbra, June 2006), Centro International de Matematica no. 28 (2006), 197--210.

-- Families of $n$-gonal curves with maximal variation of moduli (joint work with S. Gorchinskiy). Le Matematiche LXI (2006), 185-209.

-- Ramification groups and Artin conductors of radical extensions of $\mathbb{Q}$. Journal de Th\'eorie des Nombres de Bordeaux 16 (2004), 779-816.