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Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.

2 votes
2 answers
919 views

Spin Representation

I have been reading Cassels's book on "Rational Quadratic Forms". Most part of his book is written perfectly, but there is a chapter about the "Spin Representation" on his book, which I can not really …
12 votes
1 answer
2k views

Orthogonal group of quadratic form

Orthogonal group of the quadratic form over fields, somehow, is well-studied. Indeed E. Cartan has proved for quadratic forms over the reals or complexes that any orthogonal transformation is a produ …
8 votes
2 answers
2k views

Higher Composition Law

Prof M.Bhargava's work on "Higher Composition Law" which solved some outstanding conjectures on number theory seems to be very interesting topic. I have seen his papers but, in spite of the titles, it …