Barry Mazur

http://isites.harvard.edu/icb/icb.do?keyword=k28161   (no more active)
Mathematics 254 z (Spring 2005-2006)
Mathematics 254 z: Current Results in Modular Forms
Harvard College/GSAS: 0941
Spring 2005-2006
Barry C. Mazur
Meeting Time: M., W., F., at 2
A study of the background material necessary for the comprehension of some recent 
results in the theory of modular and automorphic forms, and specifically p-adic modular forms. 
The course will involve substantial student presentations.

http://isites.harvard.edu/icb/icb.do?keyword=k42401
Mathematics 223a: Algebraic Number Theory
Harvard College/GSAS: 123239
Fall 2008-2009
Barry C. Mazur and John T. Tate
Location: Science Center 109
Meeting Time: Tu., Th., 11:30-1
Exam Group: 13,14

Syllabus
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A graduate introduction to algebraic number theory. Topics: the structure of ideal class groups, 
groups of units, a study of zeta functions and L-functions, local fields, Galois cohomology, 
local class field theory, and local duality. Prerequisite: Mathematics 129.

Section
-------
There will be a fourth hour of class each week, Wednesdays 6-7pm in SC 103B. 
The time will be used as follows:
    Half an hour of discussion of the homework on weeks in which there is homework.
    Half an hour lectures by students, supplementing the main lectures and 
filling in gaps in the prerequisites or exposition.
The topics for the student lectures will be determined as the semester progresses. 
Each student will give at least one such lecture, and the lectures will affect the 
final course grade, though not as much as homework will. 
Attendance at section is mandatory for students taking the class for a grade.

Notes
-----

These files will eventually provide a (very terse) record of the topics 
that are covered in the course. We will try to keep them up-to-date.

Skeletal Notes for the Introductory Lectures
Tate Lecture 3: Group Cohomology
Adeles
Notes and exercises for Tate's 2006 lectures on Haar measure, duality
Fourier transform in adeles and ideles
Points and Ideals of small norm
Tate Lecture 4: Class Formations
L-functions
Tate Lecture 5: Class Formations, Norm Residue Symbol, Local Existence
Ways of obtaining Class Field Theory
Reciprocity Tate's Notes: "The subgroup H_K in H^2( /K; C_K)"

Student presentations
---------------------

These are the notes from the Wednesday student presentations.

Category Theory: 9_24_08 
Norms: 10_1_08
Differents and Discriminants: 10_8_08
The Upper Numbering: 10_22_08
Formal Groups: 10_29_08
Dirichlet L-series: 11_12_08

Homework
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Homework due Sept 25
Homework due Oct. 7
Homework due Oct. 14
Homework due Oct. 21
Homework due Nov. 4
Homework due Nov. 13
Homework due Nov. 25
Homework due Dec 4
Homework due Dec 16