It is well known by classical work of Douady and Hubbard that the "straightening map" from a baby Mandelbrot set to the original one is a homeomorphism (which explains why the Mandelbrot set contains infinitely many small copies of itself). The corresponding situation for parameter spaces of higher degree polynomials is much more complicated; there exists a wider variety of parameter space configurations, and the corresponding straightening maps are typically not as well-behaved. In this talk, we will consider the tricorn, the connectedness locus of quadratic antiholomorphic polynomials z^2+c. The tricorn can be viewed as a prototypical object in the parameter spaces of various families of polynomials/rational maps. Our main goal is to demonstrate that every odd period hyperbolic component of the tricorn is the basis of a "baby tricorn" (much like the corresponding phenomenon for the Mandelbrot set), but the straightening map from any "baby tricorn" to the original one is discontinuous. This is the first known example where straightening maps fail to be continuous on a real two-dimensional slice of a holomorphic family of polynomials. Speaker(s): Sabyasachi Mukherjee (Stony Brook University)