Distinguished Professor at the CUNY Graduate Center since 1999. Specialization in Commutative Algebra, Diophantine Geometry and Arithmetic Algebraic Geometry.
| Contact Information | |
|---|---|
| office | GC 4214.01 |
| phone | 212 817 8542 |
| fax | 212 817 1527 |
| lszpiro@gc.cuny.edu |
|
Distinguished Professor of Mathematics at the Graduate School University Center, City University of New York Directeur de Recherche Emerite, University of Paris-Sud, Orsay 365 Fifth Avenue, New York, NY 10016 lszpiro@gc.cuny.edu Born in Paris 23/12/1941 Doctorat d'État, University of Paris-Sud, Orsay, 1971 |
|
| Positions |
Distinguished Professor (CUNY Graduate Center) - 1999 Directeur de Recherches de Classe Exceptionnelle (CNRS at Orsay) - 1991 Maitre de Recherches, then Directeur de Recherches (CNRS at Orsay rue d'Ulm) - 1997-1991 Attaché, then Charge de Recherches (CNRS at Paris VII) - 1969-1977 Assistant, then Maitre Assistant (Sorbonne) - 1965-1977 Assistant Teacher (High School, Paris) - 1963-1965 |
| Visiting Positions | Columbia University, New York; IAS, Princeton; IMPA, Rio de Janeiro; University of Chicago; University of Todai, Tokyo; MSRI, Berkeley; TIFR, Bombay; MPI, Bonn; Mittag-Leffler Institute, Stockholm; University of Århus; Brandeis University, Waltham. |
| Awards | Fondation Doistau-Blutel (Academie des Sciences de Paris) - 1987, "For his work in Commutative Algebra and Algebraic Geometry and for his contribution to G.Faltings' proof of the Mordell conjecture." |
| Scientific Work |
The Ph.D. was written under the direction of Pierre Samuel. It was
especially influenced by seminars of C. Chevalley, A. Grothendiek and
M. Auslander. The publications range from the theory of perfect
complexes to the geometry and dynamics of heights in number theory. They
cover the following subjects: Commutative Algebra |
| Direction of Research |
Organiser of yearly seminars. Three of these seminars have been
written up and published in Astérisque (vol.86, 127, 183). Since 1999 my
seminar has been taking place at the Graduate Center in New York. Current Ph.D. students at the Graduate Center: Nikita Miasnikov, Sandra Sze, Phillip Williams, and Liang Zhao. |
| PhD's Supervised |
L. Moret-Bailly (Professor in Rennes); M. Deschamps (Professor at
University of Versailles); Shouwu Zhang (Professor at Columbia);
M. Flexor (Maitre de conferences at Orsay); E. Ullmo (Professor at
Orsay); A. Abbes (Charge de recherches at Paris-Nord); C. Gasbarri
(Professor at Roma); P. Mikkelsen (Wall Street); A. Mimar (Wall Street);
J. Pesenti (Dot-com in data mining, Philadelphia); R. Litcanu (Postdoc
in Rennes, Barcelona); J. Pineiro (Bronx Community College); M.
Majidi-Zolbanin (LaGuardia Community College, New York); M. Tepper
(Professor, University of Pennsylvania - Abingdon); Y. Baishanski
(LaGuardia Community College, New York); A. Bhatnagar (Lehman College,
New York). Editor in Chief: "Astérisque" - 1991-1993. Editor: "Bulletin de la Societe Mathematique de France" - 1984-1990. Organiser of a week every year at Oberwolfach from 1972 to 1992. Organiser of a conference in Arithmetic Geometry at Luminy in 1994. Organiser: New York Joint Number Theory Seminar, New York, 2002-present. Organiser: Algebraic Dynamics Workshop, New YOrk, 2002, 2010. Scientific Committee: European Research Counsel in Pisa, Italy, 2010. Scientific Committee: ICERM (NSF) at Brown University, "Dynamics in 2012." NSF Grants: Research Training Grant in Number Theory; Focus Research Grant in Algebraic Dynamics (with support for Post Doc and 3 students, workshops and consultations). |
| Selected Publications |
(full list of publications available here) "Dimension projective finie et cohomologie locale. Applications à la démonstation de conjectures de M. Auslander, H. Bass et A. Grothendieck," with C. Peskine. Inst. Hautes Études Sci. Publ. Math., 42, (1973), 47-119. "Liaison des variétés algèbriques," with C. Peskine. Invent. Math., 26, (1974), 271-302. "Sur la théorème de rigidité de Parshin et Arakelov," Journées de Géométrie Algèbrique de Rennes (Rennes, 1978), Vol. II. Astérisque, 64, (1979), 169-202. "Sur les propriétés numériques du dualisant relatif d'une surface arithmétique," The Grothendieck Festschrift, Vol. III. Progr. Math., 88, 229-246. Birkhäuser Boston, Boston, MA, 1990. "Équirépartition des petits points," with E. Ullmo and S. Zhang. Invent. Math., 127, (1997), 337-347. "Inégalité du discriminant pour les pinceaux elliptiques à réductions quelconques," with J. Pesenti. Compositio Math., 120, (2000), 83-117. "A Shafarevich-Faltings Theorem for rational functions," with T. Tucker. Quarterly Journal of Pure and Applied Mathematics, for the occasion of the sixtieth birthday of Fedor Bogomolov, Vol. 4 No.3, (2008), 715-728. |
| 1 | "Fonctions d'ordre et valuations," Bull. Soc. Math. France. 94, (1966), 301-311. |
| 2 | "Anneaux de Gorenstein, et torsion en algèbre commutative," Séminaire d'Algèbre Commutative dirigé par Pierre Samuel, volume 1966/67. Secrétariat Mathématique, Paris, 1967. |
| 3 | with C. Peskine. "Modules de type fini et de dimension injective finie sur un anneau local noethérien," C. R. Acad. Sci. Paris Sér. A-B, 266, (1968), A1117-A1120. |
| 4 | with C. Peskine. "Sur la topologie des sous-schémas fermés d'un schéma localement noethérien, définis comme support d'un faisceau cohérent localement de dimension projective finie," C. R. Acad. Sci. Paris Sér. A-B, 269, (1969), A49-A51. |
| 5 | Notes sur un air de Bass. Preprint Brandeis University, 1969. |
| 6 | with C. Peskine. "Sur le relèvement des modules de dimension projective finie," C. R. Acad. Sci. Paris Sér. A-B, 271, (1970), A1102-A1104. |
| 7 | with C. Peskine. "Théorèmes de finitude et de nullité en cohomologie des schémas," C. R. Acad. Sci. Paris Sér. A-B, 271, (1970), A1000-A1002. |
| 8 | "Variétés de codimension 2 dans PN," Colloque d'algèbre Commutative, 15, (1972), 7. Publ. Sém. Math. Univ. Rennes. |
| 9 | "Travaux de Kempf, Kleiman, Laksov sur les diviseurs exceptionnels," Séminaire Bourbaki, 24ème année, 417, (1971-2), 339-353. Lecture Notes in Math., 317. Springer, Berlin, 1973. |
| 10 | with C. Peskine. "Dimension projective finie et cohomologie locale. Applications à la démonstation de conjectures de M. Auslander, H. Bass et A. Grothendieck," Inst. Hautes Études Sci. Publ. Math., 42, (1973), 47-119. |
| 11 | with C. Peskine. "Liaison des variétés algèbriques," Invent. Math., 26, (1974), 271-302. |
| 12 | with C. Peskine. "Syzygies et multiplicités," C. R. Acad. Sci. Paris Sér. A., 278, (1974), 1421-1424. |
| 13 | "Cohomologie des ouverts de l'espace projectif sur un corps de caractéristique zéro (d'après A. Ogus.)," Séminaire Bourbaki, 458, (1974/5: Exposés Nos. 453-470), 81-96. Lecture Notes in Math., 514., Springer, Berlin, 1976. |
| 14 | with M. Flexor. "Un théorème de structure locale pour les complexes parfaits," Algebraic Geometry, Proc. Sympos., Univ. Tromsø, 1977. Lecture Notes in Math, 687, (1978), 236-244. |
| 15 | "Le théorème de la régularité de l'adjointe de Gorenstein à Kodaira," Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Bookstore, Tokyo, (1978), 93-102. |
| 16 | "Flâtness and Flatness," Arbeitsagung über lokale algebraische und analytische Geometrie, Münster, 1978. |
| 17 | Lectures on equations defining space curves. Tata Institute of Fundamental Research, Bombay, 1979. Notes by N. Mohan Kumar. |
| 18 | "Sur la théorème de rigidité de Parchin et Arakelov," Journées de Géométrie Algèbrique de Rennes (Rennes, 1978), Vol. II. Astérisque, 64. (1979), 169-202. |
| 19 | "Séminaire sur les pinceaux de courbes de genre au moins deux," Astérisque, 86, (1981), 1-142. |
| 20 | "Sur la théorie des complexes parfaits," Commutitative algebra: Durham 1981. London Math. Soc. Lecture Note Ser., 72, Cambridge Univ. Press, Cambridge, (1982), 83-90. |
| 21 | "Degrés, intersections, hauteurs," Astérisque, 127, (1985), 11-28. |
| 22 | "Un peu d'effectivité," Astérisque, 127, (1985), 275-287. |
| 23 | "Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell," Astérisque, 127, (1985). |
| 24 | "La conjecture de Mordell (d'après G. Faltings)," Seminar Bourbaki, 1983/4. Astérisque, 121-122, (1985), 83-103. |
| 25 | "Small points and torsion points," The Lefschetz centennial conference, Part I (Mexico City, 1984). Contemp. Math, 58, (1986), 251-260. |
| 26 | "Présentation de la théorie d'Arakelov," Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985). Contemp. Math., 67, (1987), 279-293. |
| 27 | with S. Bloch and P. Murthy. "Zero cycles and the number of generators of an ideal," Mém. Soc. Math. France (N.S.), 38, (1989), 51-74. Colloque en l'honneur de Pierre Samuel (Orsay, 1987). |
| 28 | "Discriminant et conducteur des courbes elliptiques. Séminair sur les Pinceaux de Courbes Elliptiques," Astérisque, 183, (1990), 7-18. |
| 29 | "À la recherche de 'Mordell effectif.' Séminaire sur les Pinceaux de Courbes Elliptiques," Société Mathématique de France, Paris, 1990. Astérisque, 183, (1990). |
| 30 | "Sur les propriétés numériques du dualisant relatif d'une surface arithmétique," The Grothendieck Festschrift, Vol. III. Progr. Math., 88, 229-246. Birkhäuser Boston, Boston, MA, 1990. |
| 31 | "Sur la taille des solutions de certaines équations algèbriques," Preprint Orsay. 1991. |
| 32 | "Sur les solutions d'un système d'équations polynomiales sur une variété abélienne (d'après G. Faltings et P. Vojta.)," Séminaire Bourbaki, Vol. 1989/90. Astérisque (189-90), Exp. No. 729, (1990), 429-446. |
| 33 | with D. Goldfield. "Bounds for the order of the Tate-Shafarevich group," Composition Math., Applied Mathematics, Queen's University, Kingston, ON, 1995. Special issue in honor of Frans Oort. |
| 34 | "Pierre Samuel, une influence recherchée," Collected papers of Pierre Samuel, Vol. I, II. Queen's Papers in Pure and Applied Mathematics, 99, (1995). Queen's University, Kingston, ON. |
| 35 | "Algebraic geometry over Q̄," Representation theory and algebraic geometry (Waltham, MA, 1995). London Math. Soc. Lecture Note Ser., 238, (1997), 117-123. Cambridge Univ. Press., Cambridge. |
| 36 | with E. Ullmo and S. Zhang. "Équirépartition des petits points," Invent. Math., 127, (1997), 337-347. |
| 37 | with E. Ullmo. "Variation de la hauteur de Faltings dans une classe de Q̄-isogénie de courbe elliptique," Duke Math. Journal, 97, (1999), 81-97. |
| 38 | with J. Pesenti. "Inégalité du discriminant pour les pinceaux elliptiques à réductions quelconques," Compositio Math., 120, (2000), 83-117. |
| 39 | with T. Tucker and J. Pineiro. "Mahler measure for dynamical systems on the sphere and intersection theory on a singular arithmetic surface: in number theoretic applications of algebraic geometry," Progress in Math, 235, (2004), 219-250. |
| 40 | with T. Tucker. "Algebraic dynamics," Colloquium de Giorgi 2006, Edizioni della Normale, Pisa, (2006), 51-57. |
| 41 | with T. Tucker. "One half log discriminant," Diophantine Geometry Proceedings (Publications of the Scuola Normale Superiore de Pisa), (2006), 51-57. |
| 42 | with T. Tucker. "A Shafarevich-Faltings Theorem for rational functions," Quarterly Journal of Pure and Applied Mathematics, for the occasion of the sixtieth birthday of Fedor Bogomolov, Vol. 4, No.3, (2008), 715-728. |
| 43 | with C. Petsche and M. Tepper. "Isotriviality is equivelant to potential good reduction for endomorphisms of PN over function fields," Journal of Algebra. 322, (2009), 3345-3365. |
| 44 | with T. Tucker. "Equidistribution and generalized Mahler measures," Number Theory, Analysis and Geometry: In Memory of Serge Lang, Springer (2012), 609-638. |
| 45 | with C. Petsche and T. Tucker. "A dynamical pairing between two rational maps," to appear in Transactions of the AMS, (2010). arXiv:0911.1875. |
| 46 | with A. Bhatnagar. "Very ample polarized self maps extend to projective space." Journal of Algebra, Vol. 351, Issue 1, (2012), 251-253. |
| 47 | with M. Tepper and P. Williams. "Resultant and conductor of geometrically semi-stable self maps of the projective line over a function field." (2010). arXiv:1010/5030. |
| 48 | with B. Hutz. "Almost Newton, sometimes Lattès." (2011). arXiv:1105.1695. |
| 49 | with M. Majidi-Zolbanin and N. Miasnikov. "Entropy and flatness in local algebraic dynamics." to appear in PubMath, (2013). |
| Published | "Entropy and flatness in local algebraic dynamics." with M. Majidi-Zolbanin and N. Miasnikov. to appear in PubMath, (2013). | download |
| "Almost Newton, sometimes Lattès." with B. Hutz. arXiv:1105.1696. | download | |
| "Resultant and conductor of geometrically semi-stable self maps of the projective line over a function field." with M. Tepper and P. Williams. arXiv:1010/5030. | download | |
| "Very ample polarized self maps extend to projective space." with A. Bhatnagar. Journal of Algebra, Vol 351, Issue 1, (2012), 251-253. | download | |
| "Equidistribution and Generalized Mahler Measures." with T. Tucker. Number Theory, Analysis and Geometry: In Memory of Serge Lang. Springer (2012), 609-638. | download | |
| "Isotriviality is equivalent to potential good reduction for endomorphisms of PN over function fields." with C. Petsche and M. Tepper. Journal of Algebra. 322, (2009), 3345-3365. | download | |
| "A Shafarevich-Faltings Theorem for Rational Functions." with T. Tucker. Quarterly Journal of Pure and Applied Mathematics, for the occasion of the sixtieth birthday of Fedor Bogomolov, 322, (2009), 3345-3365. | download | |
| "Algebraic Dynamics." with T. Tucker. Colloquium de Giorgi 2006, Edizioni della Normale, Pisa, (2006), 51-57. | download | |
| "One Half Log Discriminant." with T. Tucker. Diophantine Geometry Proceedings (Publications of the Scuola Normale Superiore de Pisa), 2006, 12-24. | download | |
| "Mahler measure for dynamical systems on P1 and intersection theory on a singular arithmetic surface." with T. Tucker and J. Pineiro. Progress in Math Birkhauser, (235), 2004, 219-250. | download | |
| "Inégalité du discriminant pour les pinceaux elliptiques à réductions quelconques." with J. Pesenti. Compositio Math., 120, (2000), 83-117. | download | |
| "Variation de la hauteur de Faltings dans une classe de Q̄-isogénie de courbe elliptique." with E. Ullmo. Duke Math. Journal, 97, (1999), 81-97. | download | |
| "Équirépartition des petits points." with E. Ullmo and S. Zhang. Invent. Math., 127, (1997), 337-347. | download | |
| "Algebraic Geometry Over Q̄." Representation theory and algebraic geometry (Waltham, MA, 1995). London Math. Soc. Lecture Note Ser., 238, (1997), 117-123. | download | |
| "Bounds for the order of the Tate-Shafarevich group." with D. Goldfeld. Composition Math., Applied Mathematics, Queen's University, Kingston, ON, 1995. | download | |
| "Remarques sur la taille des solutions de certaines équations algèbriques." Preprint Orsay. 1991. | download | |
| "Discriminant et conducteur des courbes elliptiques." Séminaire sur les Pinceaux de Courbes Elliptiques. Astérisque, 183, (1990), 7-18. | download | |
| "Sur les solutions d'un système d'équations polynomiales sur une variété abélienne (d'après G. Faltings et P. Vojta)." Séminaire Bourbaki, Vol. 1989/90. Astérisque (189-190), Exp. No. 729, (1990), 429-446. | download | |
| "Sur les propriétés numériques du dualisant relatif d'une surface arithmétique." The Grothendieck Festschrift, Vol. III Progr. Math., 88, 229-246. Birkhäuser Boston, Boston, MA, 1990. | download | |
| "Présentation de la théorie d'Arakelov." Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985), volume 67 of Contemporary Math., 279-293. Amer. Math. Soc., Providence, RI, 1987. | download | |
| "Zero cycles and the number of generators of an ideal." with S. Bloch and P. Murthy. Mém. Soc. Math. France (N. S.), 38, (1989), 51-74. Colloque en l'honneur de Pierre Samuel (Orsay, 1987). | download | |
| "Small points and torsion points." The Lefschetz centennial conference, Part I (Mexico City, 1984). Contemp. Math., 58, (1986), 251-260. | download | |
| "La conjecture de Mordell (d'après G. Faltings)." Séminaire Bourbaki, 1983/84. Astérisque, 121-122, (1985), 83-103. | download | |
| "Un peu d'effectivité." Astérisque, 127, (1985), 275-287. | download | |
| "La formule clé pour les schémas abéliens; applications." with L. Moret-Bailly. Astérisque, 129, (1985), 255-261. | download | |
| "Degrés, intersections, hauteurs." Astérisque, 127, (1985), 11-28. | download | |
| "Sur la théorie des complexes parfaits." Commutative algebra: Durham 1981 (Durham, 1981), volume 72 of London Math. Soc. Lecture Note Ser., pages 83-90. Cambridge Univ. Press, Cambridge, 1982. | download | |
| "Formes différentielles non fermées." Notes by R. Fossum. Astérisque, 86, (1981), 90-96. | download | |
| "Nouveaux contrexemples aux énconcés d'annulation à la Kodaira an caractéristique." Notes by M. Flexor. Astérisque, 86, (1981), 79-89. | download | |
| "Propriétés numériques du faisceau dualisant relatif." Astérisque, 86, (1981), 44-78. | download | |
| "Un théorème d'annulation en caractéristique positive." Notes by R. Ménégaux. Astérisque, 86, (1981), 35-43. | download | |
| "Sur le théorème de rigidité de Parsin et Arakelov." Journées de Géométrie Algèbrique de Rennes (Rennes, 1978), Vol. II. Astérisque, 64, (1979), 169-202. | download | |
| "Lectures on equations defining space curves." Tata Institute of Fundamental Research, Bombay, 1979. Notes by N. Mohan Kumar. | download | |
| "Flatness and flâtness." Arbeitstagung über lokale algebraische und analytische Geometrie, Münster, 1978. | download | |
| "Le théorème de la regularité de l'adjointe de Gorenstein à Kodaira." Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Bookstore, Tokyo (1978), 93-102. | download | |
| "Un théorème de structure locale pour les complexes parfaits." with M. Flexor. Algebraic geometry, Proc. Sympos., Univ. Tromsø, 1977. Lecture Notes in Math, 687, (1978), 236-244. | download | |
| "Cohomologie des ouverts de l'espace projectif sur un corps de caractéristique zéro (d'après A. Ogus)." Séminaire Bourbaki, 458, (1974/75: Exposés Nos. 453-470), 81-96. Lecture Notes in Math., 514, Springer, Berlin, 1976. | download | |
| "Liaison des variétés algèbriques." with C. Peskine. Invent. Math., 26, (1974), 271-302. | download | |
| "Syzygies et multiplicités." with C. Peskine. C. R. Acad. Sci. Paris Sér. A, 278, (1974), 1421-1424. | download | |
| "Dimension projective finie et cohomologie locale. Applications à la démonstation de conjectures de M. Auslander, H. Bass et A. Grothendieck." with C. Peskine. Inst. Hautes Études Sci. Publ. Math., 42, (1973), 47-119. | download | |
| "Travaux de Kempf, Kleiman, Laksov sur les diviseurs exceptionnels." Séminaire Bourbaki, 24ème année, 417, (1971-72), 339-353. Lecture Notes in Math., 317. Springer, Berlin, 1973. | download | |
| "Variétés de codimension 2 dans PN." Colloque d'Algèbre Commutative, 15, (1972), 7. Publ. Sém. Math. Univ. Rennes. | download | |
| "Théorèmes de finitude et de nullité en cohomologie des schémas." with C. Peskine. C. R. Acad. Sci. Paris Sér. A-B, (1970), A1000-A1002. | download | |
| "Sur le relèvement des modules de dimension projective finie." with C. Peskine. C. R. Acad. Sci. Paris Sér. A-B, (1970), A1102-A1104. | download | |
| "Sur la topologie des sous-schémas fermés d'un schéma localement noethérien, définis comme support d'un faisceau cohérent localement de dimension projective finie." with C. Peskine. C. R. Acad. Sci. Paris Sér. A-B, 269, (1969), A49-A51. | download | |
| "Modules de type fini et de dimension injective finie sur un anneau local noétherien." with C. Peskine. C. R. Acad. Sci. Paris Sér. A-B, 269, (1969), A49-A51. | download | |
| "Anneaux de Gorenstein, et torsion en algèbre commutative." Séminaire d'Algèbre Commutative dirigé par Pierre Samuel, volume 1966/67. Secrétariat Mathématique, Paris, 1967. | download | |
| "Nouvelles méthodes fonctorielles en algèbre commutative." with C. Peskine. Colloque d'Algèbre. École Normale Supérieure de Jeunes Filles. (1967), 2-01 - 2-04. | download | |
| "Fonctions d'ordre et valuations." Bull. Soc. Math. France, 94:301-311, 1966. | download | |
| Preprints | "Arkelov's intersection theory on arithmetic surfaces." (in Japanese) Preprint Arithmetic Algebraic Geometry, 1987. | download |
| "Cours de Géométrie Arithmétique." Preprint Orsay, 1986. |
download: chapter 1 chapter 2 |
|
| "Sur une demonstration elementaire du théorème d'annulation de Kodaira pour H1." Preprint 1978. | download | |
| "Méthodes homologiques en algèbre locale. Applications Géométriques." Preprint Orsay, 1970. | ||
| "A Theorem on Intersections. Application to the Demonstrations of Conjectures of M. Auslander and H. Bass." with C. Peskine. Preprint Brandeis University, 1969. | download | |
Organizers: A. Gamburd, D. Goldfeld, V. Kolyvagin, L. Szpiro, Y. Tschinkel, E. Urban.
Thursday evenings 5:00-7:00PM, rotating among Columbia University, the CUNY Graduate Center and the NYU Courant Institute.
Tea is served from 5:00-5:30PM.
RTG Seminar talk for graduate students at 4:00 PM:
The seminar will have a special RTG talk at 4:00 PM every Thursday when the seminar meets. The RTG talk will be aimed at graduate students and post-docs; regular faculty are requested not to attend.
| 2/7 | Columbia University RTG Seminar: 4:00-4:45 in Room 622 Tea: 5:00-5:30 in the 5th floor Math Lounge Number Theory Seminar: 5:30-7:00 in Room 302 |
Atsushi Ichino Kyoto University Regularized Periods of Automorphic Forms |
abstract |
| 2/14 | NYU, Courant Institute RTG Seminar: 4:00-4:45 in Room 805 Tea: 5:00-5:30 in Room 317 Number Theory Seminar: 5:30-7:00 in Room 317 |
Ehud Hrushovski Hebrew University of Jerusalem Towards a Model Theory of Global Fields |
abstract |
| 2/21 | CUNY Graduate Center RTG Seminar: 4:00-4:45 Tea: 5:00-5:30 Number Theory Seminar: 5:30-7:00 (all talks in Room 4102) |
Stephen Miller (RTG Seminar) Rutgers University Stephen Gelbart (Number Theory Seminar) Weizmann Institute, Israel On the Reciprocal of p-Adic L-Functions and p-Adic Langlands-Shahidi Integrals: the Case of SL(2) |
abstract |
| 2/28 | Columbia University RTG Seminar: 4:00-4:45 in Room 622 Tea: 5:00-5:30 in the 5th floor Math Lounge Number Theory Seminar: 5:30-7:00 in Room 302 |
Stephen Miller Rutgers University Exceptional and Larger Groups in Analytic Number Theory |
abstract |
| 3/7 | NYU, Courant Institute RTG Seminar: 4:00-4:45 in Room 805 Tea: 5:00-5:30 in Room 317 Number Theory Seminar: 5:30-7:00 in Room 317 |
Bianca Viray Brown University Using Fibrations to Study Brauer Classes on Surfaces |
abstract |
| 3/14 | CUNY Graduate Center RTG Seminar: 4:00-4:45 Tea: 5:00-5:30 Number Theory Seminar: 5:30-7:00 (all talks in Room 4102) |
Philipp Habegger Goethe-Universität, Frankfurt Small Height and Infinite Non-abelian Extensions |
abstract |
| 3/21 | Spring Break | ||
| 3/28 | Columbia University RTG Seminar: 4:00-4:45 in Room 622 Tea: 5:00-5:30 in the 5th floor Math Lounge Number Theory Seminar: 5:30-7:00 in Room 302 |
Michael Rapoport Mathematisches Institut der Universität Bonn On p-Adic Uniformization |
abstract |
| 4/4 | NYU, Courant Institute RTG Seminar: 4:00-4:45 in Room 412 Tea: 5:00-5:30 in Room 102 Number Theory Seminar: 5:30-7:00 in Room 102 Warren Weaver Hall (251 Mercer St.) |
Abhinav Kumar MIT Real Multiplication Abelian Surfaces with Everywhere Good Reduction |
abstract |
| 4/11 | CUNY Graduate Center RTG Seminar: 4:00-4:45 Tea: 5:00-5:30 Number Theory Seminar: 5:30-7:00 (all talks in Room 4102) |
Umberto Zannier Scuola Normale Superiore, Pisa Some S-unit Equations, Especially Describing Perfect Powers with Few Nonzero (Binary) Digits |
abstract |
| 4/18 | Columbia University RTG Seminar: 4:00-4:45 in Room 622 Tea: 5:00-5:30 in the 5th floor Math Lounge Number Theory Seminar: 5:30-7:00 in Room 302 |
Ellen Eischen University of North Carolina, Chapel Hill p-Adic Families of Eisenstein Series for Unitary Groups |
abstract |
| 4/25 | NYU, Courant Institute RTG Seminar: 4:00-4:45 in Room 412 Tea: 5:00-5:30 in Room 102 Number Theory Seminar: 5:30-7:00 in Room 102 Warren Weaver Hall (251 Mercer St.) |
Jim Carlson University of Utah Special Cubic Threefolds, Abelian Varieties and Totally Real Quintic Fields |
abstract |
The Joint Number Theory Seminar, held at Columbia University, the CUNY Graduate Center and the NYU Courant Institute began in Fall 2003. Meetings are held Thursdays from 5:30-7PM at one of the three colleges. For information, click here.
Thursdays, 11:00AM-1:00PM, Room 4214.03.
Note: Speakers and topics will vary each week.
Coordinator: Lucien Szpiro
Meetings are held Fridays from 12:30-1:45 in Room 3209 at the CUNY Graduate Center. For information, click here.
Co-organizers:
Gautam Chinta,
Brooke Feigon,
Maria Sabitova,
L. Szpiro.
| Past Lectures | ||
|---|---|---|
| Fourth Distinguished RTG Undergraduate Lecture | ||
| 3/12/13 | Hunter College 5:30-7:00 PM, Hunter West Room 714. |
Joseph H. Silverman Brown University Taxicabs and the Sum of Two Cubes |
| Some numbers, such as 9 = 13 + 23 and 370 = 33 + 73 can be written as the sum of two cubes. Are there numbers that can be written as the sum of cubes in two (or more) essentially different ways? This elementary question will lead us into beautiful areas of mathematics where number theory, geometry, algebra, calculus, and even internet security interact in surprising ways. | ||
| Third Distinguished RTG Undergraduate Lecture in Number Theory | ||
| 3/27/12 | Baruch College 5:30 PM, Room 6-215. |
Andrew Granville Canadian Research Chair in Number Theory Université de Montréal Pattern Hunting in the Prime Numbers |
| We will discuss patterns that have been found amongst the prime numbers, some of which we can prove are really there, and some of which are still a mystery... | ||
| Second Distinguished RTG Undergraduate Lecture in Number Theory | ||
| 3/8/11 | Hunter College 5:45 PM, Room 510. |
Ken Ono Emory University University of Wisconsin, Madison Adding and Counting |
| In mathematics, the stuff of partitions seems like mere child's play. The speaker will explain how the simple task of adding and counting has fascinated many of the world's leading mathematicians: Euler, Ramanaujan, Hardy, Rademacher, Dyson, to name a few. And as is typical in number theory, many of the most fundamental (and simple to state) questions have remained open. In 2010 the speaker, with the support of the American Institute for Mathematics and the National Science Foundation, assembled an international team of distinguished researchers to attack some of these problems. Come hear Professor Ono speak about their findings: new theories which solve some of the famous old questions. | ||
| Umbrella Seminar | ||
| 9/27/10 | CUNY Graduate Center 5:30-7:00 PM, Room 4102. |
Jan Denef Katholieke Universiteit Leuven, Belgium Geometric Proof of Ax-Kochen |
| We will sketch a new proof of the Theorem of Ax and Kochen that any projective hypersurface over the p-adic numbers has a p-adic rational point, if it is given by a homogeneous polynomial with more variables than the square of its degree d, assuming that p is large enough with respect to the degree d. Our proof is purely geometric and (unlike all previous ones) does not use methods from mathematical logic. It is based on a theorem of Abramovich and Karu about weak toroidalization of morphisms. This method also yields a proof of a conjecture of Colliot-Thelene and generalizations. An earlier, more complicated version of our proof was based on Cutkosky's Theorem on Local Monomialization of Morphisms, but to prove for example the Ax-Kochen-Ersov transfer principle along these lines we need the theorem of Abramovich and Karu. | ||
| First Distinguished RTG Undergraduate Lecture in Number Theory | ||
| 4/27/10 | Hunter College 4:00 PM, Room 714. |
Benedict Gross Leverett Professor of Mathematics Harvard University The Function n→n! |
Arithmetic Geometry Team | ||
| 2/26/09 | CUNY Graduate Center 1:30-2:30 PM, Room 4214-03 (thesis room). |
François Loeser École Normale Supérieure, Paris Some Applications of Model Theory to Algebraic Geometry |
I will illustrate the importance of the concept of definability in the study of valued fields
by three different recent applications of Model Theory to Arithmetic Geometry:
|
||
| 11/6/08 | CUNY Graduate Center 1:30 PM, Room 4214-03 (thesis room). |
Frans Oort Utrecht University, visiting Columbia Moduli Space of Abelian Variables |
| In this talk I will give a survey of my lectures at Columbia University this fall. I prove: a conjecture by Manin, a conjecture by Grothendieck, and the Hecke orbit conjecture. The emphasis will be on explaining methods about stratifications and foliations in positive characteristic, which give access to these difficult problems. | ||
| 5/1/08 | CUNY Graduate Center 2:00-4:00 PM, Room 4214-03 (thesis room). |
Yu Yasufuku Brown University Vojta's Conjecture and Blowups |
| Vojta's conjecture is a powerful conjecture in Diophantine geometry, but it is not known in most cases. In this talk, I will prove the conjecture for repeated blowups of P2 (with respect to suitably-defined integral points), using Corvaja and Zannier's result on gcd's. I will also discuss higher-dimensional cases, as well as some general relationships between Vojta's conjecture on a variety and Vojta's conjecture on its blowup. | ||
| 2/28/08 | CUNY Graduate Center 2:00-4:00 PM, Room 4214-03 (thesis room). |
Rachel Ollivier ENS Paris, visiting Columbia Mod p Representations of GL(2): from the Finite Case to the p-Adic Case. |
| Let F be a p-adic field with uniformizer π. We consider the universal module of the functions with value in F̄p and finite support on the cosets I(1)πZ\GL2(F), where I(1) denotes the pro-p-Iwahori subgroup GL2(F), it is isomorphic to the homology of level 0 of the associated coefficient system on the tree. We then use the result of [O2] to show that any representation of GL2(Qp), with a central character and generated by its pro-p-invariant subspace, is the homology of level 0 of a coefficient system on the tree. | ||
| (click on a conference title for more information) | |
| May 28 - June 1, 2012 |
Arithmetic Geometry and Arithmetic Dynamics Conference Conference on the Occasion of the 70th Birthday of Lucien Szpiro CUNY Graduate Center |
| March 19-21, 2012 |
ICERM Workshop: Global Arithmetic Dynamics Brown University |
| June 7-11, 2010 |
Algebraic Dynamics Conference CUNY Graduate Center |
| May 28-29, 2004 |
Conference on Algebraic Dynamics First Annual Mini-Conference CUNY Graduate Center |
| Information |
May 29 - June 1, 2012 The Graduate Center of the City University of New York 365 Fifth Avenue New York, NY 10016 Room 4102 |
|
| Organizers | D. Goldfeld
Columbia University V. Kolyvagin CUNY Graduate Center S. Zhang Columbia University |
|
| Abstracts | (download as pdf) | |
| Schedule | (download as pdf) | |
| 5/29 | 9:30-10:30 | David Masser Universität Basel Unlikely Intersections for Abelian Surfaces |
| 11:00-12:00 | Umberto Zannier Scuola Normale Superiore di Pisa Abelian Surfaces and Pell's Equation over Polynomial Rings |
|
| 2:00-3:00 | Joseph H. Silverman Brown University Szpiro's Conjecture with Prime Depletion and Lang's Height Conjecture |
|
| 3:30-4:30 | Thomas Tucker University of Rochester Orbits Modulo Primes and a Dynamical Mordell-Lang Conjecture |
|
| 5:00-6:00 | Emmanuel Ullmo Université de Paris 11 The Hyperbolic Ax-Lindemann Conjecture in the Compact Case and Some Applications to the André-Oort Conjecture |
|
| 5/30 | 9:30-10:30 | Luc Illusie Université de Paris 11 Quotient Stacks and Equivariant Cohomology Algebras: Quillen's Theory Revisited |
| 11:00-12:00 | Laurent Moret-Bailly Université de Rennes 1 Greenberg's Approximation Theorem and the Topology of Varieties over Valued Fields |
|
| 2:00-3:00 | Henri Gillet University of Illinois at Chicago Higher Derivations and Descent in Characteristic p |
|
| 3:30-4:30 | Christian Peskine Université de Paris 6 Smooth Linear Congruences of Lines |
|
| 5:00-6:00 | Bjorn Poonen Massachusetts Institute of Technology Random Maximal Isotropic Subspaces and Selmer Groups |
|
| 5/31 | 9:30-10:30 | José Ignacio Burgos Gil Instituto de Ciencias Matemáticas Arakelov Theory of Toric Varieties, Positivity Properties |
| 11:00-12:00 | Walter Gubler Universität Tübingen Canonical Measures and the Geometric Bogomolov Conjecture |
|
| 2:00-3:00 | Antoine Chambert-Loir Université de Rennes 1 Differential Forms and Currents on Berkovich Spaces |
|
| 3:30-4:30 | Huayi Chen Université de Paris 7 Limit Theorems in Arakelov Geometry |
|
| 6/1 | 9:30-10:30 | Jean-Benoît Bost Université de Paris 11 Algebrization of Vector Bundles on Surfaces over Number Fields |
| 11:00-12:00 | Matt Baker University of California, Berkeley Linear Series on Metrized Complexes of Algebraic Curves |
|
| 2:00-3:00 | Xinyi Yuan Princeton University Effective Bound of Linear Series on Arithmetic Surfaces |
|
| 3:30-4:30 | Atsushi Moriwaki Kyoto University Characterization of nef Arithmetic Divisors on Arithmetic Surfaces |
|
| Sponsors | National Science Foundation Graduate Center of the City University of New York |
|
| Information |
May 28-29, 2004 The Graduate Center of the City University of New York 365 Fifth Avenue New York, NY 10016 Room C198 |
|
| Organizers | D. Goldfeld
Columbia University V. Kolyvagin CUNY Graduate Center L. Szpiro CUNY Graduate Center T. Tucker University of Rochester |
|
| Schedule | (download as pdf) | |
| 5/28 | 9:00 | refreshments |
| 10:00 | W. Kelly Provost, CUNY Graduate Center opening address |
|
| 10:15 | A. Eskin University of Chicago Unipotent Flows and Branched Covers of Veech Surfaces |
|
| 2:00 | A. Chambert-Loir University of Rennes Metrized Line Bundles and Measures on Berkovich Spaces: Applications |
|
| 3:30 | P. Autissier University of Rennes Small Heights and Equidistribution |
|
| 5:00 | J. Silverman Brown University Minimal Models and Moduli Spaces for Arithmetic Dynamical Systems |
|
| 6:30 | conference dinner in Midtown | |
| 5/29 | 10:00 | R. Rumely University of Georgia Foundations of Potential Theory on the Berkovich Projective Line |
| 11:30 | M. Baker University of Georgia Equidistribution of Small Points for Dynamical Systems |
|
| 2:30 | contributed talks and open problems | |
| 6:30 | wine and cheese party on the Upper West Side | |
| Sponsors | National Science Foundation The Graduate Center Provost Research Fund The Mina Rees Chair |
|
| Current Materials | download | |
|---|---|---|
|
The Completely Decomposed Topology on Schemes and Associated Descent Spectral Sequences in Algebraic K-Theory
Y. Nasnevich, Johns Hopkins University |
||
|
Basic Arithmetic Geometry
L. Szpiro, CUNY Graduate Center based on notes by Florian Lengyel |
pdf dvi |
|
|
Cours de Géométrie Arithmétique
L. Szpiro, CUNY Graduate Center Preprint Orsay 1986 |
chapter 1 chapter 2 |
|
| Materials for Past Courses | ||
| Fall 2010 |
Algebra II course description |
|
| Spring 2010 |
Model Theory for Arithmetic Geometry course description |
|
| Spring 2009 Fall 2008 |
Algebra II course description |
doc |
| Spring 2008 |
Algebra II course description |
doc |
| Spring 2005 Fall 2004 |
Algebraic Dynamics course description |
doc |
| Fall 2005 |
Algebra II course description |
doc |
| Spring 2004 Fall 2003 |
Notes for Algebra II student notes (in progress) |
|
| index | positions available
faculty courses students summer program contact |
||
| introduction |
The National Science Foundation (NSF) has established the program: "Enhancing the Mathematical Sciences Workforce
in the 21st Century (EMSW21)," whose long-range goal is to increase the number of well-prepared U.S. citizens,
nationals, and permanent residents who pursue careers in the mathematical sciences and in other NSF-supported
disciplines. Recently, the three New York based universities: Columbia-CUNY-NYU have jointly received a 1.5
million dollar (potentially 2.5 million) RTG (Research Training Group in Number theory) grant from the NSF. The
RTG program is part of EMSW21. The goal of this Research Training Group is to make the New York metropolitan
area a premier world center and model for the study of number theory. This a joint training effort involving
three universities (Columbia-CUNY-NYU) with eight principal investigators and twenty-five other faculty all
working in number theory and related areas. We seek to provide an environment where postdocs, graduate students,
undergraduates, and faculty from the entire New York metropolitan area study and work together in a collaborative
atmosphere that fosters research and development. Number theory is one of the oldest branches of mathematics and has recently played an important role in computer science and cryptography. Recent spectacular breakthroughs in the subject such as the proof of Fermat's Last Theorem by Taylor-Wiles require an understanding of an enormous amount of mathematics, much of it outside number theory. It is not possible any more for beginning students to study a small segment of number theory. The eight PI's of this proposal (Goldfeld, Kolyvagin, Kramer, Szpiro, Tschinkel, Urban, Venkatesh, Zhang) have extensive overlapping interests but their combined expertise covers all of modern number theory. The scientific research interests of the team include algebraic/arithmetic geometry, hyperbolic geometry, automorphic forms and representations, Langlands program, analytic number theory, spectral theory, ergodic theory, Lie algebras, algebraic number theory, elliptic curves, dynamical systems, and cryptography. |
||
| positions available | Postdoctoral Positions Applications are invited for postdoctoral positions, jointly funded by the NSF RTG award Number theory, Columbia University, CUNY and the Courant Institute, NYU. NSF requires RTG fellowship recipients to be US citizens or permanent residents. The initial appointment is for a period of one year, renewable for up to two years. Applicants are requested to submit current CV, research and teaching statements, and four references through mathjobs.org. All applicants should indicate potential supervisors among the RTG faculty, and the institution (Columbia, CUNY or NYU) they would like to be their primary affiliation. The applicants should request that all letters of recommendation be submitted online, if possible. PhD Fellowships Applications are invited for doctoral fellowships, jointly funded by the NSF RTG award Number theory, Columbia, CUNY and NYU. Applications are welcome from applicants with undergraduate degrees in any related area, whose research interests and background match the interests of RTG faculty. The applications should be submitted directly to the respective PhD programs: |
||
| Columbia | CUNY | NYU | |
| While each student will have a primary host institution, the group encourages and will provide opportunities for collaboration with researchers at both universities. | |||
| NSF requires RTG fellowship recipients to be US citizens or permanent residents. International applicants interested in RTG activities are strongly encouraged to apply to the participating PhD programs, and will be considered for other sources of funding. | |||
| faculty | Principal Investigators | ||
| Columbia | CUNY | NYU | |
| Dorian Goldfeld Eric Urban Shouwu Zhang |
Victor Kolyvagin Kenneth Kramer Lucien Szpiro |
Yuri Tschinkel Akshay Venkatesh |
|
| Affiliated Faculty | |||
| Columbia | CUNY | NYU | |
| Mirela Ciperiani Patrick Gallagher Johan de Jong Yacov Kerzhner Kenneth Tignor Christian Virdol |
Michael Anshel Gautam Chinta Raymond Hoobler Bruce Jordan Jay Jorgenson Joseph Lewittes Carlos Moreno Melvyn Nathanson Kevin O'Bryant Cormack O'Sullivan Burton Randol Mark Sheingom |
Fedor Bogomolov David Harvey Sonal Jain |
|
| courses |
RTG students are required to take one designated one-semester RTG course per year. RTG Courses, Fall 2010
S. Zhang, Topics in Arithmetic Geometry RTG Courses, Fall 2008
Courses in Related Areas, Fall 2009
Courses in Related Areas, Fall 2008
M. Nathanson, Topics in Additive Number Theory F. Oort, Moduli of Abelian Varieties L. Szpiro, Algebra II: Local Cohomology Y. Tschinkel, Advanced Topics in Number Theory E. Urban, Cohomology of Arithmetic Groups and Automorphic Forms S. Zhang, Topics in Arithmetic Geometry |
||
| students/postdocs | Academic Year 2010-2011 RTG postdoctoral fellow at CUNY
RTG Ph.D. fellows at CUNY
Sandra Sze Phillip Williams Academic Year 2009-2010 RTG postdoctoral fellow at CUNY
RTG Ph.D. fellows at CUNY
Anupam Bhatnagar Phillip Williams |
||
| summer program |
The RTG also offers a summer program for undergraduates. For information, click the links below: RTG Undergraduate Summer Program 2011 RTG Undergraduate Summer Program 2010 RTG Undergraduate Summer Program 2009 |
||
| contact | For PhD admission information, please contact PhD admissions at the participating departments directly: | ||
| Columbia | CUNY | NYU | |
| For postdoctoral applications, please use mathjobs.org; please do not send your complete application materials directly to faculty, as this may delay the processing of your application. | |||
| Joseph H. Silverman Brown University Taxicabs and the Sum of Two Cubes |
|
| information | Tuesday, March 12, 2013 |
| Hunter College | |
| location | Room 714, Hunter West SW corner of 68th St. and Lexington Ave. |
| 5:30-6 PM | refreshments |
| 6-7 PM | talk |
| abstract | Some numbers, such as 9 = 13 + 23 and 370 = 33 + 73 can be written as the sum of two cubes. Are there numbers that can be written as the sum of cubes in two (or more) essentially different ways? This elementary question will lead us into beautiful areas of mathematics where number theory, geometry, algebra, calculus, and even internet security interact in surprising ways. |