Risc Colloquium
Prof. Alexander Levin: New developments in the theory of difference ideals
We will review basics of the theory of difference ideals and present an analog of R. Cohn's process of ''shuffling'' for the construction of the mixed difference ideal generated by a set. Then we will show that the ring of difference polynomials over a difference field does not satisfy the ascending chain condition for mixed difference ideals. This result solves an open problem of difference algebra stated by E. Hrushovski in connection with the development of difference algebraic geometry.