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They are 1. MAT 1128HS - Topics in Probability: The sound of sparse random graphs Instructor: Balint Virag (balint@math.toronto.edu) 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 karp...@math.jussieu.fr 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. Reference: [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 (http://www.sgs.utoronto.ca/Assets/SGS+Digital+Assets/current/Student+Forms/Reading_and_Research.pdf) 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 http://www.fields.utoronto.ca/programs/scientific/12-13/torsors/index.html Academic credit is reserved only for courses at least 12 weeks in length.

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