Mathematical Conversations | |

Topic: | Almost commuting matrices: finite- and infinite-dimensional proofs |

Speaker: | Ilya Kachkovskiy |

Affiliation: | Member, School of Mathematics |

Date: | Wednesday, April 5 |

Time/Room: | 6:00pm - 7:00pm/Dilworth Room |

I will first give an outline of Lin-Friis-Rordamâ€™s proof of the fact that almost commuting matrices are close to commuting matrices uniformly in the dimension. The proof is short and beautiful, but it involves an infinite-dimensional argument which makes it virtually impossible to recover a good qualitative distance estimate. I will discuss some "finite-dimensional" approaches to this and related problems, some of which are already known to work, some will most likely work, and some are just dreams.