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Theme Year 1998-1999

Number Theory and Arithmetic Geometry


The theme year in number theory and arithmetic geometry will emphasize several current directions: Algebraic cycles and Shimura varieties, Elliptic curves and modular forms, Representations of p-adic groups, Analytic theory of automorphic L-functions. The year will be organized around a certain number of workshops, seminar courses and mini-courses spread throughout the year. Following is a schedule of events:

Workshop on Algebraic modular forms and modular forms mod p

2-8 October 1998

The last decades have witnessed the emergence of a "Langlands philosophy mod p" which (among other things) relates Galois representations to modular forms mod p. This instructional workshop will survey this circle of ideas, with a special emphasis on (1) Gross's theory of "algebraic modular forms" and (2) the progress on Serre's conjectures arising from the work of Ribet, Taylor, and Wiles.

There will be three lecture series.

  1. B. Gross (Harvard):
    Algebraic modular forms

  2. K. Ribet (UC Berkeley):
    Congruences between modular forms

  3. S. Kudla (Maryland):
    The Siegel-Weil formula

H. Darmon (McGill and CICMA) and G. Savin (Utah)

Workshop on Analytic number theory

24-27 October 1998

The workshop will focus on recent developments in analytic number theory with special emphasis on non-vanishing theorems for L-functions attached to automorphic forms.

R. Murty (Queen's)

Invited Speakers:
K. Dilcher, J. Friedlander, S. Gonek, J. Hoffstein, H. Iwaniec, K. Murty, R. Murty, M. Nair, R. Raghunathan, C.S. Rajan, C. Stewart

CMS Winter Meeting
Special session in number theory

(Queen's Univ., Kingston, Ontario)
13-15 December 1998

R. Murty (Queen's) and N. Yui (Queen's)

Invited Speakers:
H. Darmon, C. David, J. Fabrykowski, C. Greither, H. Kisilevsky, M. Kolster, A. Ledet, C. Levesque, K. Murty, V. Platonov, D. Roy, G. Walsh, H. Williams, K. Williams

Workshop on Representations of reductive p-adic groups

9-13 May 1999

The main focus of the workshop will be construction of K-types for admissible representations, and Hecke algebras and their representations.

F. Murnaghan (Toronto)

Invited Speakers:
J. Adler, S. DeBacker, D. Goldberg, A. Helminck, C. Jantzen, P. Kutzko, D. Manderscheid, L. Morris, A. Moy, M. Reeder, B. Roberts, A. Roche, P. Sally Jr., G. Savin, J.-K. Yu

Workshop on Arithmetical algebraic geometry

14-18 May 1999

Arithmetic algebraic geometry covers a range of possible topics, and a number of graduate students will be attending the workshop, so participants have been asked to address their lectures to a wide audience and to attempt to deliver "survey talks".

M. Goresky (IAS) and K. Murty (Toronto)

Invited Speakers:
A. Baragar, D. Boyd, W. Casselman, H. Darmon, B. Gordon, M. Goresky, E. Kani, M. Kolster, J. Kramer, J. Lewis, K. Murty, M. Nori, Frans Oort, J. Scherk, N. Wieslawa, N. Yui, S.-W. Zhang

Moonshine Workshop

29 May - 4 June 1999

"Moonshine" started in 1978 with the observation that representations of some sporadic groups are naturally parametrized by the Fourier coefficients of certain modular forms. The functions arising here are axiomatizable as replicable functions from their behaviour under a generalized Hecke operator.

There is a panoply of mathematics used in these investigations. Vertex algebras, graded Lie algebras, conformal field theory, automorphic functions, Fuchsian groups, computational algebra, Schwarz derivatives, Hecke operators, representation theory, and mirror maps all appear.

The workshop, one in a two yearly series, will focus on recent developments on the subject.

J. McKay (Concordia)

Invited Speakers:
A.O.L. Atkin (Illinois, Chicago), A. Baker (Glasgow), S.J. Bloch (Chicago), M. Brightwell (Glasgow), J. Conway (Princeton), I.V. Dolgachev (Michigan), C.-Y. Dong (UC Santa Cruz), B. Dubrovin (SISSA, Trieste), P. Goddard FRS (Cambridge), G.I. Glauberman (Chicago), R.L. Griess Jr. (Michigan), K. Harada (Ohio State), M.J. Hopkins (M.I.T.), G. Mason (UC Santa Cruz), S.P. Norton (Cambridge), A.J. Ryba (Michigan), K. Saito (Kyoto), H. Tamanoi (UC Santa Cruz), M. Tuite (National University of Ireland, Galway), S.-T. Yau (Harvard), N. Yui (Queen's)

6th Conference of the Canadian Number Theory Association

(Winnipeg, Manitoba)
Co-sponsored by the CRM and The Fields Institute
20-24 June 1999

J. Borwein (Simon Fraser), D. Boyd (UBC), C. David (Concordia), R. Murty (Queen's), P. N. Shivakumar (Manitoba), C. Stewart (Waterloo), H. Williams (Manitoba)

Invited Speakers:
M. Bennett (IAS), F. Beukers (Utrecht), A. Bremner (Arizona State), D. Bressoud (Macalester College, MN), H. Darmon (McGill), J. Friedlander (Toronto), J. Grantham (Georgia), H. Kisilevsky (Concordia), M. Kolster (McMaster), H. W. Jenstra, Jr. (Berkeley), L. Merel (Paris), A. Odlyzko (AT&T Labs, NJ), K. Ono (Penn State), B. Poonen (Berkeley), D Roy (Ottawa), P. Sarnak (Princeton), W. Schmidt (Colorado), K. Soundararajan (Princeton) G. Stevens (Boston U), S. Vanstone (Waterloo), T. Wooley (Michigan, Ann Arbor)

Seminar courses

Seminar courses will last from one to three months.

Modular forms and the Birch and Swinnerton-Dyer conjecture

Elliptic and Hilbert Modular forms

The Chebotarev density theorem and some applications

An Introduction to Sieve Methods

Modular forms and the Birch and Swinnerton-Dyer conjecture

Elliptic and Hilbert Modular forms


There will be several mini-courses of two weeks each, spread throughout the year.

Iwasawa Theory of Modular Forms

Ordinary Representations and Modular Forms

Rankin-Selberg L-functions

Modular Forms and Modular Curves

Automorphic forms over function fields

Topics in p-adic Galois representations

Hilbert modular varieties

The spectrum of multiplicative values
The distribution and extreme values of L-functions

Polynomial constructions, Galois theory and elliptic curves

Representations of reductive p-adic groups

Chaire Aisenstadt Lectures

NOTE: The lectures of Professeur Andrew Wiles (Princeton), scheduled for September 1998, have been cancelled.

A Series of Lectures
Professor Frans Oort
Universiteit Utrecht
May 1999

Barsotti-Tate Groups and Newton Polygons
a proof of a conjecture by Grothendieck, Montréal 1970

Organizing Committee

Those wishing to participate in the above activities are invited to contact:

	Louis Pelletier
	CRM, Université de Montréal
	C.P. 6128, Succ. centre-ville
	Montréal (Québec) CANADA H3C 3J7

	E-mail:		ACTIVITES@CRM.UMontreal.CA
	FAX:		(514) 343-2254
	Telephone:	(514) 343-2197

18 May 1999, webmaster@CRM.UMontreal.CA