kˈɑːlɪn də vˌɜːdiˈɛɹ ɪz nˈoʊn fɔːɹ wˈɜːk ɪn spˈɛktɹəl θˈiəɹi, ɪn pɚtˈɪkjʊlɚɹ ɔnðə sˌɛmɪklˈæsɪkəl lˈɪmɪt ʌv kwˈɔntəm mᵻkˈænɪks ɪŋklˈuːdɪŋ kwˈɔntəm kˈeɪɑːs; ɪn ɡɹˈæf θˈiəɹi wˌɛɹ hiː ˌɪntɹədˈuːst ɐ nˈuː ɡɹˈæf ɪnvˈɛɹiənt, ðə kˈɑːlɪn də vˌɜːdiˈɛɹ ɡɹˈæf ɪnvˈɛɹiənt; ænd ˌɔn ɐ vɚɹˈaɪəɾi ʌv ˈʌðɚ sˈʌbdʒɛkts wɪðˌɪn ɹiːmˈæniən dʒiˈɑːmətɹi ænd nˈʌmbɚ θˈiəɹi.
Colin de Verdière is known for work in spectral theory, in particular on the semiclassical limit of quantum mechanics (including quantum chaos); in graph theory where he introduced a new graph invariant, the Colin de Verdière graph invariant; and on a variety of other subjects within Riemannian geometry and number theory.