### L-functions Program Committee:

Manfred Kolster (Department of Mathematics and Statistics, McMaster
University)

Victor Snaith (Department of Mathematics and Statistics, McMaster University)

Kumar Murty (Department of Mathematics, University of Toronto)

Ram Murty (Department of Mathematics, McGill University)

Residual activity for the number theory participants will carry on
for the period April 1, 1994 to July 31, 1995. From its inception in
September, 1993, the L-functions program was designed to apitalise on
the polarisation of research directions which were expected to arise
from the Newton Institute, Cambridge venture held in the previous academic
year. Continued advances have been made both in the theory (e.g. the
work of Kato, Kolyvagin, Rubin, Wiles and others on the Main Conjecture
of Iwasawa Theory) and in the applications (e.g. the work of Lenstra,
Van der Geer etc. on codes and primality testing). The Fields Institute
program on L-functions has been fruitful in the area of collaboration
opportuniites for the participants and many research works have geen
completed in the paset seven months as well as others in progress as
the program continues.

Workshops

### April 11-15, 1994 -- *Workshop on* *L-functions and Automorphic
Forms*

This workshop will focus on recent developments related to the search
for a general reciprocity law. This law is the central problem of number
theory and brings into focus concepts of representation theory and algebraic
geometry. The proff of the Taniyama conjecture in a large number of
cases is the most spectacular recent progress on this problem.

**March 21 - 25, 1994 -- ***Conference on L-functions*

Coordinators: Victor Snaith and Manfred Kolster (McMaster University)

**February 28 - March 4, 1994 -- ***Algebraic K-theory and Arithmetic*

Coordinators: Victor Snaith and Manfred Kolster (McMaster University)

**February 14 - 18, 1994 -- ***Algebraic K-theory and Arithmetic*

Coordinators: Victor Snaith (McMaster University)

### Courses

**September 14 - December 9, 1993 -- ***L-functions Lecture Series*

Coordinators: Victor Snaith and Manfred Kolster (McMaster University)

- Iwasawa-Theory and algebraic K-Theory (Manfred Kolster)
- L-functions and Automorphic forms (Kumar Murty)
- Basic Galois Module Structure (Victor Snaith)
- Supplement on Multiplicative Galois Module Structure (Al Weiss)

**Seminars on L-Functions**

April 28, 1994 -- Postdoctoral Seminar Series on L-Functions

John Huang (McMaster University)

Hopf Algebras and Real Projective Representations of Generalised Symmetric
Groups

April 7, 1994 --

Enric Nart (The Autonomous University of Barcelona)

Some Open Questions in Coding Theory

March 31, 1994

John Coates (Cambridge University)

Iwasawa Theory of the Symmetric Square

Fernando Q. Gouvea (Colby College, Waterville)

Deformations of Galois Representations

March 28-29, 1994

Jean-Louis Colliot-Thélène (C.N.R.S. University of Paris-South, Orsay)
Rational Points on Linear Algebraic Groups and Rationality Problems

March 28, 1994

Peter Sheneider (University of Cologne)

The Bruhat-Tits Building in Smooth Representation Theory

March 17, 1994

Uwe Jannsen (University of Cologne)

Mixed Motives, Algebraic K-theory and 1-adic Cohomology

March 15, 1994

T. Nguyen Quang Do (University of Besançon)* *

On Gross' conjecture

March 8, 10, 1994

Wayne Raskind (University of Cologne)

Algebraic K-theory, Class Field Theory and Algebraic Cycles

February 24, 1994

David Burns (King's College, London)

Tate Motives and Galois Module Structure

February 22, 1994

Martin J. Taylor (University of Manchester)

An Extended Group Scheme Workout

February 11, 1994

Philippe Cassou-Nogués (University of Bordeaux I)

The Embedding Probem and Class Number Parity

February 3, 1994

B. Sury (University of Toronto)

Work of Margulis on D

February 1, 1994

John Scherk (University of Toronto) *Lang-Weil Estimate*

December 9, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

François Destrempes (University of Toronto)

p-Divisable Groups and Reciprocity Laws

December 2, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Boris Brauckmann (McMaster University)

On the Higher Étale Tame
and Wild Kernel of a Number Field

December 2, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Michael Bean (University of Toronto)

The Number of Sulutions of the
Thue Inequality

November 18, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Hao Shen (McMaster University)* *

Torsion Algebraic Cycles for
Varieties over Local Fields

November 11, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Magdy Assem (University of Toronto)

Unipotent Orbital Integrals
on P-adic Groups

November 3, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Raymond Ross (The Fields Institute)

K of Fermat Curves with
Divisional Support at Infinity

October 27, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Xiangyong Wang (University of Alberta)* *

A Class of Integral Representations

October 20, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Shu-Leung Tang (McMaster University)

Iwasawa Theory for P-adic Representations

October 13, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Yasuhiro Goto (Queen's University)* *

On the Brauer Groups of Certain
Weighted Diagonal Surfaces

October 6, 1993 -- Postdoctoral/Graduate Student Seminar Series on
L-Functions

Werner Bley (The Fields Institute)

A Leopoldt-type Result for Rings
of Integers of Cyclotomic Extensions

September 29, 1993 -- Postdoctoral/Graduate Student Seminar Series
on L-Functions

Liem Mai (The Fields Institute)

*The Average Value of L-Functions
at the Critical Point*

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