LONGO MATTEO

Personal data.
-Born in Venice, March 24, 1976.
-Professore ordinario (Full Professor), MAT03, Dipartimento di Matematica ``Tullio Levi Civita'', via Trieste 63, 35121 Padova, Italy.

Academic positions.
-Laurea in matematica (110/110 cum laude), Università degli studi di Padova, 2000.
-Ph. D. in Mathematics, Università degli studi di Padova, 2004. (Advisor: Professor Massimo Bertolini).
-Marie Curie Fellowship, Institut de Recherche Mathématique Avancée, Strasbourg (France), 2005
-Long Term Visitor, Centre de Recherches Mathématiques, Montréal (Canada), 2005
-Marie Curie Fellowship, Max-Planck-Institut fur Mathematik Bonn (Germany), 2006
-Ricercatore universitario, Dipartimento di Matematica F. Enriques, Università degli studi di Milano Statale, 2006-2009.
-Ricercatore universitario confermato, Dipartimento di Matematica, Università degli studi di Padova, da 2009-2015.
-Visiting position at CRM, Barcelona (Spain), 2010.
-Professore associato confermato, Dipartimento di Matematica, Università degli studi di Padova, 2015-2021.
-Visiting position at IISER Pune (India), 2016.
-Visiting position at CRM, Université de Montreal (Montreal, Canada), 2017.
-Visiting position at IISER, Pune (India) 2020.
-Professore ordinario, Dipartimento di Matematica, Università degli studi di Padova, since 2021.

Research interests.
My research area is algebraic number theory. In particular, I am interested in problems related to the Birch and Swinnerton-Dyer Conjecture, one of the Millennium Problems identified by the Clay Institute. Within this field, I mainly work on p-adic variants of the Birch and Swinnerton-Dyer conjectures, including Iwasawa conjectures, attached by means of p-adic analytical tools such as the variation in p-adic families of modular forms.

Publications.
-Longo, Matteo (2023); A p-adic Maass-Shimura operator on Mumford curves. Ann. Math. Qué. 47, no. 1, 139–175.
-Longo, Matteo; Vigni, Stefano On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations. New York J. Math. 27 (2021), 437–467.
- Longo, Matteo, Pati Maria Rosaria (2021). Generalized Heegner cycles on Mumford curves. Math. Z. 297, no. 1-2, 483–515.
-Longo Matteo, Nicole Marc-Hubert (2020). Lambda-adic families of Jacobi forms, Res. Number Theory 6, paper n. 21, 24 pp.
-Longo Matteo, Martin Kimball, Hu Yan (2020). Rationality of Darmon points over genus fields of non-maximal orders. Ann. Math. Qué. 44, no. 1, 173-195.
-Longo Matteo, Vigni Stefano (2019). Kolyvagin systems and Iwasawa theory of generalised Heegner cycles. Kyoto J. Math. 59, no. 3, 717-746.
-Longo Matteo, Vigni Stefano (2019). Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes. Boll. Unione Mat. Ital., no. 3, 315-347.
-Longo Matteo, Nicole Marc-Hubert (2019). The $p$-adic variation of the Gross-Kohnen-Zagier theorem. Forum Math. 31, no. 4, 1069-1084.
-Longo Matteo, Rotger Victor, de Vera Piquero Carlos. (2018). Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture. Publ. Mat. 62, no. 2, 355-396.
-Longo Matteo, Pati Maria Rosaria (2018) Exceptional zero formulae for anticyclotomic $p$-adic $L$-functions of elliptic curves in the ramified case. J. Number Theory 190, 167-211.
-Longo, Matteo Mao, Zhengyu (2018). Kohnen's formula and a conjecture of Darmon and Tornaría. Transactions of the American Mathematical Society, vol. 370, p. 73-98.
-Longo Matteo, Castella Francesc, Kim Chan-Ho (2017). Variation of Anticyclotomic Invariants in Hida families,
Algebra Number Theory, Volume 11, Number 10, p. 2339-2368.
-Heidaryan Bahar, Longo Matteo, Peruginelli Giulio (2017). Galois structure on integral valued polynomials. Journal of Number Theory, Volume 171, p. 198-212.
-Longo Matteo, Vigni Stefano (2017). A refined Beilinson-Bloch conjecture for motives of modular forms. Transactions of the American Mathematical Society, vol. 369, p. 7301-7342.
-Castella Francesc, Longo Matteo (2016). Big Heegner points and special values of L-series. Annales Math'ematiques du Qu'ebec, vol. 40, p. 303-324.
-Longo Matteo, Vigni Stefano (2016). Quaternionic Darmon points on abelian varieties. Rivista di Matematica della Universit`a di Parma, vol. 7, p. 39-70.
-Longo Matteo, Vigni Stefano (2014). The Rationality of Quaternionic Darmon Points
Over Genus Fields of Real Quadratic Fields. International Mathematics Research Notices, vol. 13, p. 3632-3691.
-Longo Matteo, Vigni Stefano (2014). Vanishing of special values and central derivatives in Hida families. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, vol. XIII, p. 859-888.
-Longo Matteo, Nicole Marc-Hubert (2013). The Lambda-Adic Shimura-Shintani- Waldspurger Correspondence. Documenta Mathematica, vol. 18, p. 1-21.
-Longo Matteo, Nicole Marc-Hubert (2013). The Saito--Kurokawa lifting and Darmon points. Mathematische Annalen, vol. 356, p. 469-486.
-Longo Matteo, Rotger Victor, Vigni Stefano (2013). Special values of L-functions and the arithmetic of Darmon points. Journal fur die Reine und Angewandte Mathematik, vol. 684, p. 199-244.
-Longo Matteo, Rotger Victor, Vigni Stefano (2012). On rigid analytic uniformization of Jacobians of Shimura curves. American Journal of Mathematics, vol. 134, p. 1197-1246.
-Longo Matteo (2012). Anticycotomic Iwasawa's Main Conjecture for Hilbert modular forms. Commentarii Mathematici Helvetici, vol. 87, p. 303-353.
-Longo Matteo, Vigni Stefano (2012). A note on Control Theorems for quaternionic Hida families of modular forms. International Journal of Number Theory, vol. 8, p. 1425-1462.
-Longo Matteo, Vigni Stefano (2011). Quaternion algebras, Heegner points and the arithmetic of Hida families. Manuscripta Mathematica, vol. 135, p. 273-328.
-Balasubramanyam Baskar, Longo Matteo (2011). $Lambda$-adic modular symbols over totally real fields. Commentarii Mathematici Helvetici, vol. 86, p. 841-865.
-Longo Matteo, Vigni Stefano (2010). On the vanishing of Selmer groups for elliptic curves over ring class field. Journal of Number Theory, vol. 130, p.128-163.
-Longo Matteo, Vigni Stefano (2010). An irreducibility criterion for group representations with arithmetic applications. Proceedings of the American Mathematical Society, vol. 138, p. 3437-3447.
-Longo Matteo (2007). Euler systems obtained from congruences between Hilbert modular forms. Rendiconti del Seminario Matematico dell'Università di Padova, vol. 118, p. 1-34.
-Longo Matteo (2006). On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields. Annales de l'institut Fourier, vol. 56, p. 689-733.

Administration.
-Senato Accademico, Università degli Studi di Padova, member, 2015-2019
-Ph.D. School in Mathematics, Università degli Studi di Padova, member, since 2017.
-Scientific committee of the Department of Mathematics, Padova, member 2018-2022.
-Scientific committee of the University of Padova, member 2016-2019, coordinator 2020-2024.

Conferences:
-CMS 75th Anniversary Summer Meeting, Ottawa, 5-8 Giugno 2021 (one line).
-Number Theory Day, IISER Pune (India), 2020.
-p-adic modular forms, 31-esima edizione delle Journées Arithmetiques, Istanbul, 2019.
-p-adic modular forms and p-adic L-functions, Como, Italy, 2019.
-Special Values of Automorphic L-functions and Associated p-adic L-Functions, CMO-BIRS, Oaxaca, Mexico, 2018.
-Worshop on p-adic L-functions and algebraic cycles. Taipei (Taiwan), 2017.
-Automorphic Motives, Euler Systems and p-adic L-functions, Nisyros island, 2017.
-Représentations p-adiques et fonctions L, Bordeaux (Francia) 2016.
-Terzo Incontro Italiano di Teoria dei Numeri, Pisa, 2015.
-p-adic Hodge theory and Iwasawa theory, Bielefeld, Germania, 2015.
- p-adic methods in the theory of classical automorphic forms, CRM Montreal (Ca). 2015.
- Workshop on Galois Representations, Heidelberg, 2015.
-p-adic Methods in Number Theory, Università Statale di Milano, 2014.
-Arithmetic intersection theory and Shimura varieties, Hausdorff Research Institute of Mathematics, Bonn, 2014.
-Effective methods for Darmon points, Benasque, 2013.
-Modular forms, p-adic L-functions and Selmer groups, Oriahovitza, 2013.
-Cycles on modular varieties, BIRS, Banff, Alberta, Canada,2011.
-Special Values of L-functions and Arithmetic Geometry, Miyama, Japan. 2010.
-Giornate di geometria algebrica ed argomenti correlati IX'', Levico Terme (Trento), 2008.
-International Conference on Arithmetic Algebraic Geometry, El Escorial, Spagna, 2006.

Organization of schools an workshops
-Elliptic curves and modular forms in arithmetic geometry, Milano, 2022.
-Recent advances in the arithmetic of Galois representations, Genova, 2019,
-Organization of the session S20 Number Theory at Conferenza UMI 2019, Pavia, 2019.
-p-adic Langlands Program in Padova, 2019
-Serre Conjectures and p-adic Langlands Program, Padova, 2019.
-Summer School and Workshop on Modular forms, Padova, 2017.
-Perfectoid Spaces, Brixen 2015
-Algant Summer School on Monodromy, Dobbiaco, 2014.

Seminars
-Number Theory Seminar, Kolyvagin Conjecture and Bloch-Kato formula for modular forms, Dublin, Ireland., 2022.
-Number Theory Seminar, Kolyvagin Conjecture and Bloch-Kato formula for modular forms, Poznan, Polony, 2020.
-Number Theory Seminar, Anticyclotomic Iwasawa Main Conjectures for elliptic curves, Regensburg, Germany, 2018.
-The Quebec-Vermont number theory seminar (Montreal, Canada), On the p-adic variation of the Gross-Kohnen-Zagier Theorem, 2017.
-Oberseminar, University of Duisburg-Essen (Germany), On the p-adic variation of the Gross-Kohnen-Zagier Theorem, 2017.
-Number Theory Seminar, Tate Institute, Mumbay (India), Anticyclotomic Iwasawa main conjecture for elliptic curves, 2016.
-The Mathematics Colloquium at Rutgers (Newark Univ., NJ, USA), Heegner Points and Arithmetic of Elliptic Curves, 2014.
-UCLA Colloquium of the Department of Mathematics (University of California, Los Angeles, USA),
Heegner points and the arithmetic of elliptic curves: classical results and generalizations, 2012.
-UCLA Number Theory Seminar University of California, Los Angeles, USA, Quaternionic Darmon points and arithmetic applications,2012.
-Séminaire Groupes Réductifs et Formes Automorphes, Institut de Math. de Jussieu (Parigi, Francia),
Saito-Kurokawa lifting and Darmon points, 2012.
-Quebec-Vermont Number Theory Seminar, McGill University (Montreal, Canada), Variation of Gross-Heegner points in Hida families, 2011.
-Number Theory Seminar, Max-Planck-Institut fur Mathematik (Bonn, Germania), Quaternionic Darmon points and arithmetic applications, 2011.
-Seminar de Teoria de Nombres, CRM (Barcelona, Spagna) On rigid analytic uniformization of Jacobians of Shimura curves and applications, 2010.
-Seminar de Teoria de Nombres, U. Politècnica de Catalunya (Barcelona, Spagna) On the Birch and Swinnerton-Dyer conjecture for elliptic curves over ring class fields, 2008.
-Seminaire de Théorie des Nombres, Institut Fourier (Grenoble, Francia), p-adic L-functions in two variables attached to nearly ordinary families of Hilbert modular forms, 2008.
- Number Theory Seminar, Max-Planck-Institut fure Mathematik, (Bonn, Germania), On the Birch and Swinnerton-Dyer conjecture over totally real fields, 2006.
-Centre de Recherches Mathématiques (Montréal, Canada), On the Birch and Swinnerton-Dyer conjecture over totally real fields, 2005.

Grants
-Progetto di Ateneo PRAT 2013 Arithmetic of varieties over number fields, CPDA135371/13, 31.000 euro, 2014-2018.
-Post-doc position: Big Heegner points and generalised Heegner cycles on Shimura curves, 2020-2021.
- Post-doc position: p-adic L-functions and generalized Heegner cycles, 2018-2019.
-Post-doc position: Anticylotomic Iwasawa Main Conjecture at ramified primes, 2016-2018.
-Grant (Visiting Scientist position), Prof. Marc-Hubert Nicole, 2017.
-Grant (Visiting Scientist position), Prof. Baskar Balasubramanyam (ISEER Pune, India), 2017.

Teaching.
Ph.D. Thesis
-Eduardo Walchek (Padova, XXXVI ciclo).
-Shilun Wang (Padova XXXVI ciclo and CSC, Chinese Scholarship Council).
-Daniele Troletti (Padova, XXXV ciclo). On the $p$-part of the Birch and Swinnerton-Dyer Conjeture for elliptic curves over totally real fields, 2023.
-Luca Mastella (Padova, XXXV ciclo). On Iwasawa Theory of modular forms and structure theorems of Selmer groups, 2023.
-Hu Yan (Padova, XXXI ciclo). Rationality of Darmon points over genus fields of non-maximal orders. 2019
-Guhanvenkat Harikumar (Padova, XXVII ciclo, Algant Ph.D.), Darmon cycles and the Kohnen - Shintani lifting, 2018
Master
-Francesco Zerman, The Iwasawa Main Conjecture for elliptic curves and its applications to Birch and Swinnerton-Dyer conjecture, a.a. 2019-2020, Padova.
-Lorenzo Stefanello, Euler systems and Iwasawa Theory: A proof of the Main Conjecture, a.a. 2019-2020, Padova.
-Casper Barendrecht, Shafarevich-Tate groups for some Modular Abelian Varieties. a.a. 2019-2020, Padova.
-Giuseppe Romanazzi, Rational points on elliptic curves, a.a. 2019-2020, Padova.
-Alessandro Guaglianone, Fattorizzazione di interi e algoritmo di Lenstra, a.a. 2019-2020, Padova.
-Ersilia Silvestri, Complex multiplication on elliptic curves, a.a. 2018-2019, Padova.
-Luca Lovato,Stark's Conjecture, a.a. 2018-2019, Padova.
-Alberto Busatto, Homology and Cohomology for orientable manifolds, a.a. 2017-2018, Padova.
-Alessia Trovò, Un'introduzione all'Ultimo Teorema di Fermat, a.a. 2017-2018, Padova.
-Chiara Dellantonio, Solvable points on elliptic curves, a.a. 2015-2016, Padova.
Antonio Cauchi, Kolyvagin's method for modular curves, a.a. 2013-2014, Padova.
-Gabriele Bogo, A refined Birch and Swinnerton-Dyer conjecture, a.a. 2013-2014, Padova.
-Anna Stawska, Beilinson's formula, Algant Master Thesis, a.a. 2013-2014, Padova.
-Dipayan Chakraborty, Mordell-Weil Theorem and the Birch and Swinnerton-Dyer Conjecture, Algant Master Thesis, a.a. 2011-2012, Padova.

Tesi di laurea triennale:
-Erik Chinellato, Il gruppo fondamentale di un grafo e applicazioni alla teoria dei gruppi, a.a. 2019-2020, Padova.
-Giulia Fontanella, Introduzione all'omologia singolare, a.a. 2017-2018, Padova.
-Simone Pelizzola, Curve ellittiche e numeri congruenti, a.a. 2017-2018, Padova.
-Giacomo Negrisolo, Un'introduzione alle forme modulari: il problema dei quattro quadrati, a.a. 2017-2018, Padova.
-Massimo Cosimo, Curve ellittiche e numeri congruenti, a.a. 2017-2018, Padova.
-Giacomo Vianello, Il gruppo fondamentale di un grafo, a.a. 2017-2018, Padova.
-Marco Dall'Alba, Introduzione all'omologia singolare e applicazioni al gruppo fondamentale, a.a. 2017-2018, Padova.
-Giulia Cicognani, Moduli su anelli principali, a.a. 2016-2017, Padova.
-Ilaria Prosepe, Introduzione alla teoria algebrica dei numeri, a.a. 2016-2017, Padova.
-Daniele Troletti, Il teorema dei quattro quadrati, a.a. 2016-2017, Padova.
-Luca Lovato, Teoria di Galois infinita, a.a. 2016-2017, Padova.
-Flavio Perissinotto, Il Problema dei Numeri Cogruenti, a.a. 2016-2017, Padova.
-Ersilia Silvestri, Il Teorema dei quattro quadrati, a.a. 2016-2017, Padova.
-Giada Volpato, Introduzione alla teoria dell'omologia singolare, a.a. 2015-2016, Padova.
-Giovanni Niero, Risolubilità per radicali reali, a.a. 2015-2016, Padova.
-Roberto Moreschini, Decompsizione di primi in campi ciclotomici, a.a. 2015-2016, Padova.
-Alberto Corato, Forme modulari, a.a. 2015-2016, Padova.
-Riccardo Falconi, Le Curve Modulari, a.a. 2015-2016, Padova.
-Beatrice Stivanello, Teoria di Galois infinita, a.a. 2014-2015, Padova.
-Francesco Delfina, Teoria di Galois delle algebre étale, a.a.2014-2015, Padova.
-Claudia Dario, eoria di Galois dei polinomi reciproci, a.a. 2013-2014, Padova.
-Nicola Simionato, Il teorema di Kronecker-Weber, a.a. 2013-2014, Padova.
-Pietro Gatti, Curve ellittiche e numeri congruenti, a.a. 2012-2013, Padova.
-Marina Casson, L'Ultimo Teorema di Fermat, a.a. 2011-2012, Padova.

Algebra Lineare, Ingegneria Padova.
Dall'a.a. 2010-2011 all'a.a. 2020-2021 ho tenuto corsi di algebra lineare e geometria per i corsi di laurea in Ingegneria dell'Energia, Ingegneria Edile-Architettura, Ingegneria Industriale e Ingegneria Chimica e dei Materiali.

Geometria II, Matematica, Padova.
Durante l'a.a. 2020-2021 tengo, in collaborazione con Ernesto Mistretta, il modulo B del corso di Geometria II per la laurea triennale in matematica, Padova.

Topologia, Matematica Padova.
Dall'a.a. 2015-2016 all'a.a. 2019-2020 ho tenuto il corso di Topologia per la laurea triennale in matematica, Padova.

Algebraic Geometry II, Padova.
Durante l'a.a. 2014-2015 ho tenuto, in collaborazione con Marco Garuti, il corso di Geometria Algebrica II alla laurea magistrale in matematica, Padova.

Formazione degli insegnanti, Milano.
Durante il periodo in cui sono stato Ricercatore Universitario all'Università Statale di Milano, mi sono occupato
dei corsi di formazione per insegnanti delle scuole medie inferiori e superiori e dei relativi
esami di stato -- Corsi Speciali ex DM 85, Indirizzo SN (Scienze Naturali) e FIM (Fisica e Matematica). I corsi che ho tenuto negli a.a. 2007-2008, 2008-2009-2009-2010 sono: Geometria I e II, Matematica di Base, Complementi di Matematica, Algebra ed Aritmetica II, Matematica II.