Organizers 
Andreas Rosenschon and Anand Sawant

Time and place 
Wednesdays 1416 in Room B 252.

Short description 
We will study basics of Witt and GrothendieckWitt groups of a commutative ring and their relationship with projective modules over the ring.
As an application of these methods, we will study some of the recent results on freeness of stably free modules over certain rings.

Literature 
 P. Balmer: Witt groups. Handbook of Ktheory. Vol. 1, 2, 539576, Springer, Berlin, 2005. Link
 M. Schlichting: Hermitian Ktheory of exact categories. J. KTheory 5 (2010), no. 1, 105165.
 J. Fasel, R. A. Rao and R. G. Swan: On stably free modules over affine algebras. Publ. Math. Inst. Hautes Études Sci. 116 (2012), 223243.

News 
 The seminar will be conducted in English. The first meeting will be on May 3, 2017.
 The seminar is intended for Master students (prerequisites: commutative algebra and algebraic geometry).
 There will be no lecture on June 28.

Plan of lectures 
 May 03: Lecture 1: Overview of the topics that will be covered in the seminar; organization. (Anand Sawant)
 May 10: Lectures 2,3: Introduction to quadratic forms and Witt groups. (Claudia Stadlmayr, Killian Rückschloß)
 May 17: Lecture 4: Introduction to algebraic Ktheory. (Tariq Syed)
 May 24: Lectures 5,6: Witt groups of an exact category with duality. (Ismail AchmedZade, Killian Rückschloß)
 May 31: Lecture 7: Hermitian Qconstruction and the GrothendieckWitt space of an exact category with duality. (Monica Flamann)
 June 07: Lecture 8: Unimodular rows and the Vaserstein symbol  I. (Tariq Syed)
 June 14: Lecture 9: Unimodular rows and the Vaserstein symbol  II. (Tariq Syed)
 June 21: Lecture 10: Completion of some unimodular rows. (Andrei Lavrenov)

 Proof of the FaselRaoSwan theorem. (3 lectures, Anand Sawant)
 July 05: Lecture 11: Structure of the proof and reductions.
 July 12: Lecture 12: GrothendieckWitt groups of affine schemes, Karoubi periodicity theorem and the GerstenGrothendieckWitt spectral sequence.
 July 19: Lecture 13: Divisibility of certain GrothendieckWitt groups and completion of proof.
