Prof. Lucien Szpiro

Lucien Szpiro

Distinguished Professor
CUNY Graduate Center PhD Program in Mathematics


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
email

Curriculum Vitæ

Lucien Szpiro

(download as .pdf)

  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


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
Projective Geometry
Geometry of surfaces fibered over a curve
Arithmetic Geometry (discriminants and conductors of elliptic curves, rational points)
Algebraic Dynamics
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.
 

Publications

Lucien Szpiro

(download as .pdf)

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 ," 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 -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).
 

Papers

Lucien Szpiro

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
 
Columbia-CUNY-NYU Joint Number Theory Seminar

New York Joint Number Theory Seminar

Spring 2013


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.

Information on past seminars can be found here.

 
10/9 CUNY Graduate Center

Number Theory Seminar (Pirutka): 4:30-5:30
Tea: 5:30-6:00
Number Theory Seminar (Oh): 6:00-7:00
(no RTG talk; all talks in Room 4102)
Alena Pirutka
École Polytechnique

On Integral Versions of the Tate Conjecture
abstract
Hee Oh
Yale University

TBA
 
10/16 Simultaneous Ritt Lecture and Joint Number Theory Lecture at
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 312
Manjul Bhargava
Princeton University

TBA
 
10/23 NYU, Courant Institute
Warren Weaver Hall (251 Mercer St.)

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
John Voight
Dartmouth College

TBA
 
10/30 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)
Zhengyu Mao
Rutgers-Newark

TBA
 
11/9 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 312
Cristian Popescu
University of California, San Diego

TBA
 
11/13 NYU, Courant Institute
Warren Weaver Hall (251 Mercer St.)

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
TBA


TBA
 
10/30 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)
A. Raghuram
IISER Pune

Special Values of Automorphic L-functions and Congruences
abstract
 
11/27 Thanksgiving
(no seminar)
 
 
12/4 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 312
TBA


TBA
 
12/11 NYU, Courant Institute

Warren Weaver Hall (251 Mercer St.)

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
Warren Weaver Hall (251 Mercer St.)
TBA


TBA
 
12/18 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)
Matt Young
Texas A&M and IAS

TBA
 

Seminars

Columbia-CUNY-NYU Joint Number Theory Seminar

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.

Impromptu Seminar in Arithmetic Geometry

Thursdays, 11:00AM-1:00PM, Room 4214.03.

Note: Speakers and topics will vary each week.

Coordinator: Lucien Szpiro

Collaborative Number Theory Seminar at the CUNY Graduate Center

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.


Lectures and Conferences

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:
  1. Proving global results on p-adic functions without using the mean-value theorem nor connectedness (joint work with R. Cluckers and G. Comte).
  2. A generalization of Ax-Kochen-Ersov for integrals (joint work with R. Cluckers).
  3. Berkovich spaces as pro-definable sets (joint work with E. Hrushovski).
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.
 

Past Conferences

 (click on a conference title for more information)
May 28 - June 1, 2012
March 19-21, 2012
June 7-11, 2010
May 28-29, 2004
 

Arithmetic Geometry and Arithmetic Dynamics Conference

Conference on the Occasion of the 70th Birthday of Lucien Szpiro

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
Columbia University


CUNY Graduate Center


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
 

Conference on Algebraic Dynamics

First Annual Mini-Conference

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
Columbia University


CUNY Graduate Center


CUNY Graduate Center


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
 

Course Materials

Current Materials download
The Completely Decomposed Topology on Schemes and Associated Descent Spectral Sequences in Algebraic K-Theory
Y. Nasnevich, Johns Hopkins University
pdf
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
pdf
Spring 2010 Model Theory for Arithmetic Geometry
course description
pdf
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)
pdf
 

Research Training Group in Number Theory

Columbia-CUNY-NYU

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

RTG Courses, Fall 2008

Courses in Related Areas, Fall 2009
    M. Nathanson, Additive Number Theory

Courses in Related Areas, Fall 2008
    A.J. de Jong, Research Seminar
    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
    Benjamin Hutz

RTG Ph.D. fellows at CUNY
    Nikita Miasnikov
    Sandra Sze
    Phillip Williams

Academic Year 2009-2010

RTG postdoctoral fellow at CUNY
    Yu Yasufuku

RTG Ph.D. fellows at CUNY
    Yelena Baishanski
    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.
 

Fourth Distinguished RTG Undergraduate Lecture in Number Theory

  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.