Georgia Institute of Technology College of Sciences

This special algebra seminar will feature short talks by our very own May Cai and Matt Baker, who will speak on the following topics: 

May Cai: The completion problem asks one to take a partial observation of some underlying object, and try to recover the original observation. Concretely, we have some object of interest, and a point in the image of that object under a projection map, and want to understand the fiber of this point under this map. In particular, for log-linear models, which are the restrictions of toric varieties to the probability simplex, under certain mild conditions, when this fiber is finite it turns out to have exactly either one or two entries. This is joint work with Cecilie Olesen Recke and Thomas Yahl.

Matt Baker: The determinant of a skew-symmetric matrix has a canonical square root given by the Pfaffian. Similarly, the resultant of two reciprocal polynomials of even degree has a canonical square root given by their reciprocant. Computing the reciprocant of two cyclotomic polynomials yields a short and elegant proof of the Law of Quadratic Reciprocity.