hiː dɪvˈaɪzd fɪltɹˈeɪʃənz ɪn hˈɑːpf ˈældʒᵻbɹəz ænd ðə bˈʌtʃsteɪbɚ spˈɛktɹəl sˈiːkwəns, wˌɪtʃ wɜː səksˈɛsfəli ɐplˈaɪd tə ðə kˌælkjʊlˈeɪʃən ʌv stˈeɪbəl hˈɑːməɾəpi ɡɹˈuːps ʌv sfˈɪɹz.
He devised filtrations in Hopf algebras and the Buchstaber spectral sequence, which  were successfully applied to the calculation of stable homotopy groups of spheres.