Laurentiu Maxim, University of Wisconsin-Madison: Linear optimization via Chern-Mather classes

Laurentiu Maxim, University of Wisconsin-Madison: Linear optimization via Chern-Mather classes
The linear optimization degree gives an algebraic measure of the complexity of optimizing a linear objective function over an algebraic model. Geometrically, it can be interpreted as the degree of a projection map on the affine conormal variety. I will first explain how the geometry of this conormal variety, expressed in terms of its bidegrees, completely determines the Chern-Mather classes of the given affine variety. Moreover, these bidegrees are shown to coincide with the linear optimization degrees of generic affine sections. Relations to polar geometry and the nearest point problem will also be discussed. (Based on joint work with J. Rodriguez, B. Wang and L. Wu.)