Richard Sommer CSLI, Ventura Hall, Stanford University, Stanford, California 94305-4115 sommer@csli.stanford.edu Title: The Computational Complexity of Uniform Reflection We present a mathematical (complexity-theoretic) characterization of the metamathematical principle of uniform reflection. In particular, we will state results asserting that, over elementary recursive arithmetic (ERA), the uniform $\Sigma^0_1$-reflection principle for $T$ (i.e., the assertion that every $T$-provable $\Sigma^0_1$-formula is true) is equivalent to the assertion of the totality of a specific function in the fast-growing hierarchy, for various commonly studied subsystems $T$ of first- and second-order arithmetic. Also, statements in the hierarchy generated by iterating uniform $\Sigma^0_1$-reflection, starting with ERA, correspond exactly to statements of totality of functions in the fast-growing hierarchy.