hiː wɛnt tə ðə kˌælɪfˈoːɹniə ˈɪnstɪtˌuːt ʌv tɛknˈɑːlədʒi fɔːɹ dˈɑːktɚɹəl stˈʌdi ɪn mˌæθɪmˈæɾɪks, ænd kəmplˈiːɾᵻd hɪz pˌiːˈeɪtʃ.dˈiː. ɪn nˈaɪntiːnhˈʌndɹɪd ˈeɪɾi sˈɛvən, wɪððə dɪsɚtˈeɪʃən ɹᵻsˈoːɹsbˈaʊndᵻd kˈæɾɪɡɚɹi ænd mˈɛʒɚɹ ɪn ˌɛkspənˈɛnʃəl kəmplˈɛksᵻɾi klˈæsᵻz sˈuːpɚvˌaɪzd baɪ ˌælɪɡzˈændɚɹ ˈɛs. kˈɛkɹɪs.
He went to the California Institute of Technology for doctoral study in mathematics, and completed his Ph.D. in 1987, with the dissertation Resource-Bounded Category and Measure in Exponential Complexity Classes supervised by Alexander S. Kechris.