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  1.  MAT 1128HS - Topics in Probability: The sound of sparse random graphs
      Instructor:  Balint Virag (

This is a course about eigenvalues of various models of sparse random
graphs. We will cover the basic theory of random Schrodinger operators
(boxes on Z^d with randomly weighted loops added at each vertex), as well
as Erdos-Renyi graph models and random regular graphs.

Grading. Based on problems and student projects/presentations

Tentatively scheduled for 
Tuesdays 12:30 - 1:30 pm, in BA 6183
Thursdays 2:00 - 4:00 pm, in BA 6180
First Class:  Tuesday, January 8, 2013

2.  Fields Institute Graduate Course: Algebraic and Geometric Theory of 
    Quadratic Forms (part of the Fields Thematic Program on  
    Torsors, Nonassociative Algebras and Cohomological Invariants)
    Instructor: Nikita Karpenko, Dean's Distinguished Visitor, University of Toronto

 Following [1, Part 1], we develop the basics of the theory of quadratic forms over arbitrary fields. In the second half of the course we briefly introduce the Chow groups and then apply them to get some of more advanced results of [1, Part 3].

Here is the program in more details:
1. Bilinear forms.
2. Quadratic forms.
3. Forms over rational function fields.
4. Function fields of quadrics. 
5. Forms and algebraic extensions.
6. u-invariants.
7. Applications of the Milnor conjecture.
8. Chow groups. 
9. Cycles on powers of quadrics.
10. Izhboldin dimension.

[1] R. Elman, N. Karpenko, A. Merkurjev.
    The Algebraic and Geometric Theory of Quadratic Forms.
    American Mathematical Society Colloquium Publications, 
    56. American Mathematical Society, Providence, RI, 2008. 435 pp.  

Organizational Meeting:  
Tuesday, January 8, 2013, 5:00 p.m, Stewart Library, Fields Institute

Students wishing to take this course will enrol with the course number
MAT 1901HS and will use a reading course form

The program also offers a couple of short courses:

January-March 2013
Graduate course on Affine and Extended Affine Lie Algebras
Lecturer: Erhard Neher

January-February 2013
Graduate course on Algebraic Groups over arbitrary fields
Lecturers: Vladimir Chernousov and Nikita Semenov

March 1 -April 27, 2013
Graduate Course on Reductive group schemes
Lecturer: Philippe Gille

For more information, please visit

Academic credit is reserved only for courses at least 12 weeks in length.

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