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Abstract: The theory of quadratic forms dates back at least to Pythagoras and continues to flourish today. In the talk the subject will be introduced from scratch --- starting from the basic definitions --- and connections with other areas of mathematics will be mentioned briefly. Then some fundamental problems will be stated, and special attention will be given to these problems over the field Q of rational numbers and the ring Z of integers; and also to the analogous theory over the rational function field k(x) --- where k is a finite field --- and its interesting subrings.
This talk will be accessible to graduate students.
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