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.
POSITIONS
-- POST-DOC POSITION at Mittag-Leffler Institute of Stockholm, September 2006--June 2007.
In the academic year 2006/2007, I had a post-doc position at the Mittag-Leffler Institute of Stockholm,where I participated at the special year on \emph{Moduli spaces} under the direction of
prof. T. Ekedhal and prof. C. Faber.
-- POST-DOC POSITION at the H\"umboldt University of Berlin, September 2007--December 2008.
From September 2007 till December 2008, I had a post-doc position
at the H\"umboldt University of Berlin, where I partecipated in the International Research Training Group
\emph{Arithmetic and Geometry}, under the supervision of prof. G. Farkas and prof. J. Kramer.
-- 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.
FELLOWSHIPS, AWARDS and GRANTS
-- Post-Doc at the Mittag-Leffler Institute, Stockholm (Sweden).
-- 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).
-- 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).
RESEARCH INTERESTS
-- ALGEBRAIC GEOMETRY: Moduli spaces. Tropical Geometry. Birational Geometry. Geometry invariant theory. Intersection theory on stacks.
-- NUMBER THEORY: Finite group schemes and p-divisible groups. Algebraic number theory.
-- ALGEBRA: Lie algebras. Combinatorial commutative algebra.
PAPERS
-- \emph{Slope inequalities for KSB-stable and K-stable families} (joint with G. Codogni, L. Tasin). Proc. London Math. Society 126 (2023), 1394--1465.
-- \emph{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.
-- \emph{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.
-- \emph{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.
-- \emph{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.
-- \emph{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.
-- \emph{A support theorem for Hilbert schemes of planar curves, II} (joint with L. Migliorini, V. Schende). Compositio Math. 157 (2021), 835--882.
-- \emph{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.
-- \emph{Moduli and periods of supersymmetric curves} (joint with G. Codogni). Advances in Theoretical and Mathematical Physics, Vol. 23, No. 2 (2019), pp. 345--402.
-- \emph{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.
-- \emph{Fourier-Mukai and autoduality for compactified Jacobians II} (joint with M. Melo, A. Rapagnetta). Geometry and Topology 23-5 (2019), 2335--2395.
-- \emph{Fourier-Mukai and autoduality for compactified Jacobians I} (joint with M. Melo, A. Rapagnetta). J. Reine Angew. Math. 755 (2019), 1-65.
-- \emph{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.
-- \emph{Fine compactified Jacobians of reduced curves} (joint with M. Melo, A. Rapagnetta). Trans. Amer. Math. Soc. 369 (2017), no. 8, 5341--5402.
-- \emph{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.
-- \emph{The local structure of compactified Jacobians} (joint work with S. Casalaina-Martin, J. L. Kass). Proc. London Math. Soc. 110 (2015), 510--542.
-- \emph{Geometric invariant theory for polarized curves} (joint with G. Bini, F. Felici, M. Melo). Lecture Notes in Mathematics 2122 (2014).
-- \emph{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).
-- \emph{The Picard group of the compactified universal Jacobian} (joint with M. Melo). Documenta Mathematica 19 (2014), 457--506.
-- \emph{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.
-- \emph{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.
-- \emph{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.
-- \emph{Comparing perfect and 2nd Voronoi decompositions: the matroidal locus} (joint work with M. Melo). Math. Ann. 354 (2012), no. 4, 1521–-1554.
-- \emph{Restricted infinitesimal deformations of restricted simple Lie algebras}. J. Algebra Appl. 11 (2012), no. 5, 1250091, 19 pp.
-- \emph{Fine compactified Jacobians} (joint work with M. Melo). Math. Nachr. 285 (2012), no. 8-9, 997--1031.
-- \emph{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.
-- \emph{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.
-- \emph{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.
-- \emph{Torelli theorem for stable curves} (joint with L. Caporaso). J. Eur. Math. Soc. (JEMS) 13 (2011), no. 5, 1289--1329.
-- \emph{On the tropical Torelli map} (joint work with S. Brannetti, M. Melo). Advances in Mathematics 226 (2011), 2546-2586.
-- \emph{Torelli theorem for graphs and tropical curves} (joint work with L. Caporaso). Duke Mathematical Journal Vol.153, no. 1 (2010), 129--171.
-- \emph{Simple finite group schemes and their infinitesimal deformations}. Rend. Sem. Mat. Univ. Politec. Torino Vol. 68 (2010), 171--182.
-- \emph{A note on families of hyperelliptic curves} (joint work with S. Gorchinskiy). Archiv der Mathematik 92 (2009), 119-128.
-- \emph{Deformations of the restricted Melikian Lie algebra}. Communications in Algebra 37 (2009), no. 7, 1850--1872.
-- \emph{Infinitesimal deformations of simple restricted Lie algebras II}. Journal of Pure and Applied Algebra 213 (2009), 1702-1721.
-- \emph{Cohomological support loci for Abel-Prym curves} (joint work with S. Casa\-laina-Martin and M. Lahoz). Le Matematiche LXIII (2008), 205--222.
-- \emph{Infinitesimal deformations of simple restricted Lie algebras I}. Journal of Algebra 320 (2008), 4102--4131.
-- \emph{Deformazioni di algebre di Lie semplici ristrette.} Matematica nella Societ\`a e nella Cultura 1 (2008), no. 2, 371--374.
-- \emph{Picard group of moduli of hyperelliptic curves} (joint work with S. Gorchinskiy). Mathematische Zeitschrift 258 (2008), 319--331.
-- \emph{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.
-- \emph{Families of $n$-gonal curves with maximal variation of moduli} (joint work with S. Gorchinskiy). Le Matematiche LXI (2006), 185-209.
-- \emph{Ramification groups and Artin conductors of radical extensions of $\mathbb{Q}$}. Journal de Th\'eorie des Nombres de Bordeaux 16 (2004), 779-816.
PREPRINTS
-- \emph{On the Picard group scheme of the moduli stack of stable pointed curves} (joint with R. Fringuelli). Preprint arXiv:2005.06920.
-- \emph{On a new class of fine compactified Jacobians of nodal curves.} Preprint arXiv:2310.20317.
-- \emph{The line bundles on the moduli stack of principal bundles on families of curves.} (joint with R. Fringuelli). Preprint arXiv:2401.02204.
EDITORIAL ACTIVITY
-- \emph{Moduli of K-stable Varieties.} Editors: Codogni, Giulio, Dervan, Ruadhai, Viviani, Filippo.
\href{https://link.springer.com/book/10.1007/978-3-030-13158-6}{Springer INdAM Series, Volume 31.}
DOI: 10.1007/978-3-030-13158-6.
SUPERVISION OF GRADUTE STUDENTS AND POSTDOCS
Supervision of the following \emph{PhD students} from the University of Roma Tre:
-- Fabio Felici, PhD Thesis defended the 5th May 2014, Title of the PhD thesis: ``GIT of Hilbert and Chow schemes of curves''.
-- Roberto Fringuelli, PhD Thesis defended the 16th June 2017, Title of the PhD thesis: ``The Picard group of the universal moduli space of vector bundles on stable curves and the abelian Franchetta conjecture for abelian varieties''.
\item Michele Savarese, PhD Thesis defended the 29th April 2019, Title of the PhD thesis: ``Moduli spaces of coherent sheaves on primitive multiple curves''.
-- Raffaele Carbone., PhD Thesis defended on the 19th March 2020, Title of the PhD thesis: "The Norm map on the compactified Jacobian, the Prym stack and spectral data for G-Higgs pairs".
-- Davide Gori, PhD student (of Rome La Sapienza) at the first year.
Supervision of the following \emph{PostDoc} fellows:
-- Ethan Cotterill, PostDoc at the University of Coimbra, October 2011--March 2013.
-- Giulio Codogni, PostDoc at the University of Roma Tre, February 2014--July 2017.
-- Francesco Bastianelli, PostDoc at the University of Roma Tre, June 2014--June 2016.
INSTITUTIONAL RESPONSIBILITIES
-- Organizer of the Geometry Seminar at the University of Roma Tre, 2009--2020.
Webpage: \href{http://ricerca.mat.uniroma3.it/users/geometria/seminarigeometria.html}{http://ricerca.mat.uniroma3.it/users/geometria/seminarigeometria.html}
-- 2010--present: Member of the Faculty of the PhD program at the University of Roma Tre.
INVITED COURSES ON INTERNATIONAL ADVANCED SCHOOLS
-- Course on \emph{Moduli Spaces of Curves and Abelian Varieties.}
Research School Pragmatic 2015 on ``Moduli of curves and line bundles'', Catania (Italy), 22 June -- 10 July 2015.
Webpage: \href{https://www.dmi.unict.it/pragmatic/docs/Pragmatic2015.html}{https://www.dmi.unict.it/pragmatic/docs/Pragmatic2015.html}
-- Course on \emph{Toroidal compactifications and tropicalizations of moduli spaces}.
CIME-CIRM Course on ``Combinatorial Algebraic Geometry'', Levico Terme (Trento, Italy), 10--15 June 2013.
Webpage: \href{http://web.math.unifi.it/users/ottavian/cimecirmcag/cimecirmcag.html}{http://web.math.unifi.it/users/ottavian/cimecirmcag/cimecirmcag.html}
-- Course on \emph{The Torelli morphism and the Torelli theorem}.
School ``Curves and Jacobians: state of the art'', Levico Terme (Trento, Italy), 13--16 February 2013.
Webpage: \href{http://www.science.unitn.it/cirm/Curves2013.html}{http://www.science.unitn.it/cirm/Curves2013.html}
CONFERENCES ORGANIZED
-- AIM Workshop \emph{Developments in moduli problems.} 27 February-1 March 2023
Webpage: \href{https://aimath.org/pastworkshops/moduliproblems.html}{https://aimath.org/pastworkshops/moduliproblems.html}
-- Conference \emph{Algebraic Geometry in Roma Tre} (a conference on the occasion of Sandro Verra's 70(+2)th birthday), Roma Tre University, 14-17 June 2022.
Webpage: \href{http://ricerca.mat.uniroma3.it/users/moduli/verra70}{http://ricerca.mat.uniroma3.it/users/moduli/verra70}
-- AIM(=American Institute of Mathematics) Workshop: \emph{Moduli problems beyond geometric invariant theory}, online workshop, 25-29 January 2021.
Webpage: \href{https://aimath.org/workshops/upcoming/newmethodmoduli}{https://aimath.org/workshops/upcoming/newmethodmoduli}
-- Conference \emph{Geometry in Pairs}, Roma Tre University, 19-20 December 2019.
Webpage: \href{http://ricerca.matfis.uniroma3.it/AeneasConference2018/GeometryInPairs2019/index.html}{http://ricerca.matfis.uniroma3.it/AeneasConference2018/GeometryInPairs2019/index.html}
-- Coordinator of the Algebraic Geometry Session at the \emph{XXI Congresso dell'Unione Matematica Italiana}, University of Pavia, 2-9 September 2019.
Webpage: \href{http://umi.dm.unibo.it/congresso2019/programma/sezioni-speciali/s18-geometria-algebrica/s18-giovedi-5-settembre/}{http://umi.dm.unibo.it/congresso2019/programma/sezioni-speciali/s18-geometria-algebrica/s18-giovedi-5-settembre/}
-- INdAM Workshop \emph{Moduli of K-stable varieties}, INdAM (Roma), 10--14 July 2017.
Webpage: \href{http://ricerca.mat.uniroma3.it/users/codogni/moduliconference}{http://ricerca.mat.uniroma3.it/users/codogni/moduliconference}
-- \emph{An induction day to Super-Geometry}, University of Roma Tre, 23 April 2014.
Webpage: \href{http://ricerca.mat.uniroma3.it/users/codogni/SuperDay.html}{http://ricerca.mat.uniroma3.it/users/codogni/SuperDay.html}
-- \emph{Minicourses on Stability}, University of Coimbra, 10-12 April 2014.
Webpage: \href{http://www.mat.uc.pt/~stab/index.html}{http://www.mat.uc.pt/$\sim$stab/index.html}
-- Conference \emph{G\'eom\'etrie alg\'ebriques en libert\'e XVIII}. Coimbra (Portugal), 8--12 June 2010.
-- Conference \emph{G\'eom\'etrie alg\'ebriques en libert\'e XVII}. Lorentz center, Leiden (Netherlands),
8--12 June 2009.
Webpage: \href{http://www.lorentzcenter.nl/lc/web/2009/326/info.php3?wsid=326}
{http://www.lorentzcenter.nl/lc/web/2009/326/info.php3?wsid=326}
TEACHING ACTIVITIES
I taught several courses starting from 2009 at the University of Roma Tre (for a complete list see
\href{http://ricerca.mat.uniroma3.it/users/viviani/didattica.html}{http://ricerca.mat.uniroma3.it/users/viviani/didattica.html}), among which the following PhD courses:
-- 2009: Differential Topology, \href{http://ricerca.mat.uniroma3.it/users/viviani/GE5.html}{http://ricerca.mat.uniroma3.it/users/viviani/GE5.html}
-- 2010: Geometric invariant theory, \href{http://ricerca.mat.uniroma3.it/users/viviani/GIT.html}{http://ricerca.mat.uniroma3.it/users/viviani/GIT.html}
-- 2012: Toroidal compactifications of locally symmetric varieties,
\href{http://ricerca.mat.uniroma3.it/users/viviani/Toroidal.html}{http://ricerca.mat.uniroma3.it/users/viviani/Toroidal.html}
-- Graph Theory, \href{http://ricerca.mat.uniroma3.it/users/viviani/grafi.html}{http://ricerca.mat.uniroma3.it/users/viviani/grafi.html}
-- 2014: Elements of Geometric invariant theory with applications to Moduli (joint with I. Morrison), \href{http://ricerca.mat.uniroma3.it/users/viviani/GIT2014-15.html}{http://ricerca.mat.uniroma3.it/users/viviani/GIT2014-15.html}
-- 2017: Selected topics on K3 surfaces, \href{http://ricerca.mat.uniroma3.it/users/viviani/K3.html}{http://ricerca.mat.uniroma3.it/users/viviani/K3.html}
Talks at INTERNATIONAL CONFERENCES:
-- \emph{On a new class of fine compactified Jacobians of nodal curves.} ``Derived Workshop", Bonn, 6-10 November 2023.
-- \emph{On a new class of fine compactified Jacobians of nodal curves.} Workshop ``Algebraic geometry in Bologna", Bologna, 26-28 September 2023.
-- \emph{On the Picard group of the stack of G-bundles on families of curves}.
Workshop ``Geometric and Arithmetic Frontiers of Orbifolds II - Arithmetic and hyperbolicity", Strasbourg, 5-9 June 2023.
-- \emph{On the Picard group of the stack of G-bundles on families of curves}. Workshop ``Moduli and Algebraic Cycles", Mittag-Leffler, 29 May-2 June 2023.
-- \emph{On the Universal Jacobian: algebraic, tropical and logarithmic aspects.} Workshop ``Logarithmic geometry and moduli spaces'', Frankfurt, 22-24 February 2023.
-- \emph{The Picard group of the universal moduli stack of principal bundles on pointed curves}. School on Mirror Symmetry and Moduli Spaces, Lisbon, 27 June-1 July 2022.
-- \emph{On the Universal Jacobian: algebraic, tropical and logarithmic aspects}. Conference ``Moduli spaces and logarithmic geometry", Mittag-Leffler Institute (Stockholm), 15-19 Novembre 2021.
-- \emph{Slope inequalities for KSB-stable and K-stable families}, Conference ``Riposte Armonie", Cetraro, 21-24 September 2021.
-- \emph{On the Universal Jacobian: algebraic, tropical and logarithmic aspects.} Conference ``Brill-Noether theory: geometric, tropical and singularity theory aspects", Humboldt University of Berlin, 5-7 November 2019.
-- \emph{On the Universal Jacobian: algebraic, tropical and logarithmic aspects.} Workshop on Discrete geometry with a view on symplectic and tropical geometry, University of Cologne, 23-27 September 2019.
-- \emph{On the cone of effective cycles on the symmetric products of curves.} ``Basel-Dijon-EPFL birational geometry meeting", Lausanne, 3--4 May 2018.
-- \emph{On the cone of effective cycles on the symmetric products of curves.} Workshop ``Sheaves, curves, and moduli", Stavanger (Norway), 16--20 April 2018.
-- \emph{On the cone of effective cycles on the symmetric products of curves.} Korean-Italian Meeting on Algebraic Geometry 2018, 8--12 January 2018.
-- \emph{On the cone of effective cycles on the symmetric products of a curve.} Conference ``31 Col\'oquio Brasileiro de Matem\'atica", IMPA (Rio de Janiero), 30 July--5 August 2017.
-- \emph{The cohomology of the Hilbert scheme and of the compactified Jacobians of a singular curve.} Conference ``Algebraic Geometry and Representation Theory in Rome'', Roma La Sapienza, 22 December 2016.
-- \emph{The cohomology of the Hilbert scheme and of the compactified Jacobians of a singular curve.} Conference ``Moduli and Birational geometry V'', Jeju (South Korea), 12--16 December 2016.
-- \emph{The cohomology of the Hilbert scheme and compactified Jacobians.} Workshop ``Combinatorial Moduli Spaces'', Fields Institute (Toronto), 5-9 December 2016.
-- \emph{Macdonald formula for singular curves.} Workshop ``Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics'', ICERM (Brown University, Providence), 1--5 August 2016.
-- \emph{Macdonald formula for singular curves.} Conference ``Geometry of Algebraic Varieties 2016'', Levico Terme (Trento), 20--25 June 2016.
-- \emph{Fourier-Mukai and autoduality for compactified Jacobians.} Conference ``Classification of Projective Varieties", Levico Terme (Trento), 31 August -- 4 September 2015.
-- \emph{Fourier-Mukai and autoduality for compactified Jacobians.} AMS Summer Institute in Algebraic Geometry, University of Utah, Salt Lake City, 21 July 2015.
-- \emph{Fourier-Mukai and autoduality for compactified Jacobians.} BC-Northeastern Algebraic Geometry Conference, Northeastern University (Boston), 25 April 2015.
-- \emph{GIT of Hilbert schemes of curves.} Workshop ``Birational geometry and stability of moduli stacks and spaces of curves''. Vietnam Institute for Advanced Studies in Mathematics, Vietnam, 9 February -- 1 March 2014.
-- \emph{On the cone of Moriwaki divisors.} ``Georgia Algebraic Geometry Symposium'', Athens (Georgia, USA), 18--20 October 2013.
-- \emph{Tropicalizing vs Compactifying the Torelli map}.
Conference on ``Tropical aspects in Geometry and Topology''. MPIM, Bonn, 2--6 September 2013.
-- \emph{Fourier-Mukai transform and autoduality for compactified Jacobians}. Conference ``Moduli and Birational Geometry'', Postech (Pohang, Korea), 12--16 August 2013.
-- \emph{Autoduality and Fourier-Mukai for degenerations of Jacobians}, Colloquium GRIFGA, Strasbourg, 4--6 March 2013.
-- \emph{Autoduality and Fourier-Mukai for degenarations of Jacobians.} Conference
``15 years of Pragmatic'', Catania, 17--19 September 2012.
-- \emph{Autoduality and Fourier-Mukai transform for compactified Jacobians of singular curves.} School ``Introduction to Geometric Langlands'', Freiburg, 30 July--3 August 2012.
-- \emph{Comparing toroidal compactifications of the moduli space of abelian varieties.}
Workshop Tropical Geometry, ICMS (Edinburgh), 2--6 April 2012.
-- \emph{On GIT quotients of Hilbert and Chow schemes of curves.} Workshop
``Algebraic Geometry III to II'', Roma Tor Vergata, 16--17 February 2012.
-- \emph{Linear series on tropical curves}. Workshop Perspectives in Tropical Geometry 2011, Arolla (Switzerland), 18--21 July 2011.
-- \emph{Tropical Teichm\"uller theory}. Workshop on Tropical and Toric Geometry, Trento, 12--17 September 2011.
-- \emph{On cographic toric face rings}. I Latin American School of Algebraic Geometry and Applications (ELGA 2011), Cordoba (Argentina), 8--12 August 2011.
-- \emph{GIT of Hilbert and Chow schemes of curves.} Workshop on Moduli and birational geometry, Gyeongju, South Korea, 11--15 July 2011.
-- \emph{Cohomology of categories fibered in groupoids.} VIII Portuguese Category Theory, Coimbra, 17 May 2011.
-- \emph{Tropical moduli spaces. } Bellairs workshop in Number Theory on Tropical and non-archimedean geometry,
Bellairs Research Institute (Barbados), 6--13 May 2011.
-- \emph{The Torelli Map: Compactification And Tropicalization.} I Meeting Coimbra-Salamanca Algebraic Geometry Seminar,
Coimbra (Portugal), 29--30 January 2010.
-- \emph{On the tropical Torelli map.} Workshop Tropical geometry in combinatorics and algebra. MSRI (Berkeley), 12--16 October 2009.
-- \emph{Torelli theorem for stable curves.} School and Conference on Moduli. Humboldt University of Berlin, 21--28 August 2009.
-- \emph{Deformations of restricted simple Lie algebras in positive characteristic.} XVIII Latin American Algebra Colloquium,
Hotel Fonte Colina Verde, S\~ao Pedro, (SP, Brazil), 3--8 August 2009.
-- \emph{Torelli theorem for stable curves}. Seminar at 27th Brazilian Mathematics Colloquium,
IMPA (Rio de Janeiro), 27--31 July 2009.
-- \emph{Torelli theorem for stable curves}. Seminar at the
Conference "G\'eom\'etrie alg\'ebriques et g\'eom\'etrie complexe", CIRM (Luminy), 12--16 January 2009.
-- \emph{Torelli theorem for singular curves}. Seminar at the
workshop de Investigadores J\'ovenes 2008, Madrid, 26 September 2008.